prof. dr hab. inż. Zenon Mróz

 Zakład Mechaniki Materiałów (ZMM) Pracownia Mikromechaniki Materiałów (PMM) emeryt telefon: (+48) 22 826 12 81 wew.: 139 pokój: 136 e-mail: zmroz strona www: http://bluebox.ippt.pan.pl/~zmroz/

##### Doktorat
1959Nośność graniczna i kształtowanie wytrzymałościowe płyt i powłok
 promotor -- prof. dr hab. inż. Wacław Olszak, IPPT PAN
20
##### Habilitacja
 1964-05 O formie związków fizycznych w teorii plastyczności
##### Profesura
 1971 Nadanie tytułu naukowego profesora
##### Inne
 1986 Członek korespondent Polskiej Akademii Nauk 2004 Członek rzeczywisty Polskiej Akademii Nauk

##### Promotor prac doktorskich
 1 2003-10-27 Białas Marcin Modelowanie rozwoju uszkodzeń w warstwach kontaktowych materiałów 2 1996-12-19 Piekarski Jarosław Wrażliwość i projektowanie optymalne nieliniowych układów sprężystych 3 1996-11-28 Stupkiewicz Stanisław Modelowanie poślizgów i rozwoju uszkodzeń w strefie kontaktu ciał sprężysto-plastycznych 524 4 1996-11-28 Maciejewski Jan Analiza stanów pokrytycznych w procesach urabiania gruntów 5 1993-12-16 Kowalczyk Maciej Analiza stanów pokrytycznych w układach sprężystych i niesprężystych 6 1993-12-16 Rodzik Piotr Deformacja plastyczna metali przy zmiennych obciążeniach 7 1991-01-03 Buczyński Andrzej  (PW) Stany graniczne w ośrodkach krucho-plastycznych 8 1989 Jarzębowski Andrzej Modele konstytutywne dla materiałów rozdrobnionych i ich zastosowanie 9 1988-07-12 Bojczuk Dariusz  (PŚ) Analiza wrażliwości i optymalizacja kształtu konstrukcji 10 1988 Nawrocki Paweł Inicjacja tąpań górotworu jako zagadnienie utraty stateczności 11 1985 Klisiński Marek Degradacja i odkształcenia plastyczne betonu 12 1983 Wertyński Andrzej Zastosowanie modelu ze wzmocnieniem anizotropowym do analizy procesu zagęszczenia gruntu 13 1982 Lekszycki Tomasz Optymalne projektowanie układów lepko-sprężystych 14 1980 Szeląg Daniel Optymalizacja konstrukcji sprężystych przy zmiennych warunkach podparcia 15 1979 Pietruszczak Stanisław Problemy brzegowe dla sprężysto-plastycznych modeli gruntów 16 1978 Kujawski Daniel Plastyczne i lepkie efekty przy cyklicznej deformacji metali 17 1976 Dragon Andrzej Mechanika ośrodków kruchoplastycznych z wewnętrznymi parametrami zniszczenia 18 1974 Hueckel Tomasz Teoria sprężysto-plastycznych materiałów rozdrobnionych o zmiennej gęstości 19 1974 Goss Czesław Opis wzmocnienia plastycznego metali przy złożonych obciążeniach cyklicznych 20 1973 Grzymkowski Marian Osiowo-symetryczne zagadnienia obróbki plastycznej metali 21 1971 Izbicki Ryszard Płaskie i osiowosymetryczne zagadnienia nośności granicznej w mechanice gruntów i skał 22 1970 Szymański Czesław Przepływy dynamiczne ośrodków rozdrobnionych w zbieżnych kanałach 23 1969 Bojanowski Witold  (PŁ) Badanie warunku plastyczności i praw płynięcia ośrodka sypkiego 24 1968 Drescher Andrzej Badanie własności reologicznych gruntów spoistych

##### Ostatnie publikacje
 1 Moallemi S., Pietruszczak S., Mróz Z., Deterministic size effect in concrete structures with account for chemo-mechanical loading, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2016.10.003, Vol.182, pp.74-86, 2017Moallemi S., Pietruszczak S., Mróz Z., Deterministic size effect in concrete structures with account for chemo-mechanical loading, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2016.10.003, Vol.182, pp.74-86, 2017Abstract:The work presented here is focused on examining the size effect in concrete structures subjected to different loading conditions, which include a chemo-mechanical interaction. The study involves extensive three dimensional finite element simulations, which incorporate a constitutive law with embedded discontinuity for tracing the propagation of damage pattern. The analysis deals with various mechanical scenarios that incorporate both a cohesive and frictional damage mechanism, as well as the effects of degradation of concrete triggered by continuing alkali-silica reaction (ASR). In the latter case, a chemo-plasticity framework is employed. The first set of simulations provides a deterministic assessment of the size effect in a series of three-point bending tests as well as compression tests. For continuing ASR, it is demonstrated that, by increasing the size of the structure, a spontaneous failure may occur under a sustained load. The numerical examples given here clearly show that the size effect is associated with propagation of localized damage whose rate is controlled by a suitably defined ‘characteristic length’.Keywords:Size effect, Alkali-silica reaction, 3D crack propagation, Embedded discontinuity model, Bifurcation analysis 40p. 2 Korol E., Tejchman J., Mróz Z., Experimental and numerical assessment of size effect in geometrically similar slender concrete beams with basalt reinforcement, ENGINEERING STRUCTURES, ISSN: 0141-0296, DOI: 10.1016/j.engstruct.2017.03.011, Vol.141, pp.272-291, 2017Korol E., Tejchman J., Mróz Z., Experimental and numerical assessment of size effect in geometrically similar slender concrete beams with basalt reinforcement, ENGINEERING STRUCTURES, ISSN: 0141-0296, DOI: 10.1016/j.engstruct.2017.03.011, Vol.141, pp.272-291, 2017Abstract:The paper presents a comprehensive experimental and numerical analysis of slender rectangular reinforced concrete beams with longitudinal BFRP bars without shear reinforcement subjected to 3-point bending. The experiments included 4 different beams which were similar in two directions. The main research objective was to investigate the size effect on the nominal shear strength of beams. The detailed experimental analysis of beam strength, failure mode and cracking evolution was presented and compared with previous test results on beams reinforced by ordinary steel bears. The experiments with BFRP bars were numerically reproduced using the 2D finite element method based on a coupled elastic-plastic-damage formulation. In order to describe strain localization in concrete, a non-local constitutive model was applied with account for a characteristic length of micro-structure developing in the softening regime. The numerical results were in satisfactory agreement with the experimental data. Advantages and disadvantages of BFRP reinforcement in concrete beams were next outlined.Keywords:BFRP bars, Concrete, Elastic-plastic-damage, Non-local softening, Shear, Size effect, Strain localization 35p. 3 Balevičius R., Mróz Z., Analytical Modelling of Combined Slip and Sliding Modes in Contact Interaction of Two Spherical Grains, Procedia Engineering, ISSN: 1877-7058, DOI: 10.1016/j.proeng.2017.02.020, Vol.172, pp.75-82, 2017Balevičius R., Mróz Z., Analytical Modelling of Combined Slip and Sliding Modes in Contact Interaction of Two Spherical Grains, Procedia Engineering, ISSN: 1877-7058, DOI: 10.1016/j.proeng.2017.02.020, Vol.172, pp.75-82, 2017Abstract:The analytical modelling of coupled slip and sliding contact response of two elastic spheres is presented for the kinematically imposed sphere centre relative motion trajectories. One sphere is assumed as a fixed, the other translating along a specified trajectory and remaining in contact condition. Two cases are considered, the first is corresponding to a linear trajectory with the contact engagement in the combined slip-sliding mode, the other is related to the contact initiation by normal loading and subsequent motion along an inclined linear trajectory. The formulae and diagrams of the evolution of driving force along the sliding path in terms of main contact geometry parameters were analytically specified. Further extensions and applications of the analysis can be envisaged in the creation of the translation controlled apparatus for the measurements of friction and restitution coefficients for the pair of spherical grains.Keywords:soil, spherical grains contact interaction, slip and finite sliding modes, monotonic or reciprocal sliding, coefficients of friction and restitution 4 Ziętek G., Mróz Z., A constitutive hardening model of coupled plastic deformation and martensitic transformation in steels, MECHANICS OF MATERIALS, ISSN: 0167-6636, DOI: 10.1016/j.mechmat.2016.06.004, Vol.100, pp.154-166, 2016Ziętek G., Mróz Z., A constitutive hardening model of coupled plastic deformation and martensitic transformation in steels, MECHANICS OF MATERIALS, ISSN: 0167-6636, DOI: 10.1016/j.mechmat.2016.06.004, Vol.100, pp.154-166, 2016Abstract:The article presents a constitutive model aimed at simulation of martensitic transformation induced by stress and plastic strain coupled with the hardening process in austenitic steels. The yield and transformation conditions are assumed to depend on back stresses evolving during plastic deformation and transformation processes. Their interaction affects essentially the hardening rate of a material. The thermodynamic background is reviewed and applied with both free energy and dissipation functions used in derivation of the rules of flow, hardening and transformation kinetics. The constitutive model parameters are specified and next the simulation of strain hardening for monotonic and cyclic loading is presented for the cases of uniaxial tension-compression and for combined tension-torsion deformation programs. The effect of strain ratcheting is analyzed for the cases of uniaxial and combined loading. It is shown that the transformation process is shown to essentially reduce the ratcheting strain.Keywords:Martensitic transformation, Plastic deformation, Back stresses, Yield and transformation conditions, Hardening rates 40p. 5 Giusti S.M., Mróz Z., Novotny A.A., Sokołowski J., Topology design of thermomechanical actuators, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-016-1593-0, pp.1-13, 2016Giusti S.M., Mróz Z., Novotny A.A., Sokołowski J., Topology design of thermomechanical actuators, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-016-1593-0, pp.1-13, 2016Abstract:The paper deals with topology design of thermomechanical actuators. The goal of shape optimization is to maximize the output displacement in a given direction on the boundary of the elastic body, which is submitted to a thermal excitation that induces a dilatation/contraction of the thermomechanical device. The optimal structure is identified by an elastic material distribution, while a very compliant (weak) material is used to mimic voids. The mathematical model of an actuator takes the form of a semicoupled system of partial differential equations. The boundary value problem includes two components, the Navier equation for linear elasticity coupled with the Poisson equation for steady-state heat conduction. The mechanical coupling is the thermal stress induced by the temperature field. Given the integral shape functional, we evaluate its topological derivative with respect to the nucleation of a small circular inclusion with the thermomechanical properties governed by two contrast parameters. The obtained topological derivative is employed to generate a steepest descent direction within the level set numerical procedure of topology optimization in a fixed geometrical domain. Finally, several finite element-based examples for the topology design of thermomechanical actuators are presented.Keywords:Shape-topology optimization, Topological derivative, Thermomechanical devices, Optimum design 35p. 6 Páczelt I., Mróz Z., Analysis of Wear Processes for Periodic Loading, KEY ENGINEERING MATERIALS, ISSN: 1662-9795, DOI: 10.4028/www.scientific.net/KEM.681.117, Vol.681, pp.117-141, 2016Páczelt I., Mróz Z., Analysis of Wear Processes for Periodic Loading, KEY ENGINEERING MATERIALS, ISSN: 1662-9795, DOI: 10.4028/www.scientific.net/KEM.681.117, Vol.681, pp.117-141, 2016Abstract:In the paper a class of wear problems is considered, for which the contact zone is fixed on one of contacting bodies and translates on the surface of another body, like in the case of punch in relative translation on a substrate. In the case of constant normal loads interacting with the induced monotonic sliding, the steady state wear process is reached. In the case of fixed normal load and the reciprocal sliding condition the wear process tends to its steady periodic state. Similarly, for periodically varying normal load, a steady periodic state is reached for the case of monotonic sliding. A most general case occurs for in-phase or out-of-phase periodic variation of normal load interacting with the reciprocal sliding. The paper is aimed to provide further study of steady wear states by considering periodically varying normal load combined with monotonic or alternating sliding conditions. The illustrative examples demonstrate the contact pressure and wear distribution in steady states with application to brake wear analysis.Keywords: Contact Problems, Periodic Loading, Periodic Steady-States, p-Version of Finite Elements, Sliding Wear 7 Syroka-Korol E., Tejchman J., Mróz Z., FE investigations of the effect of fluctuating local tensile strength on coupled energetic-statistical size effect in concrete beams, ENGINEERING STRUCTURES, ISSN: 0141-0296, DOI: 10.1016/j.engstruct.2015.09.011, Vol.103, pp.239-259, 2015Syroka-Korol E., Tejchman J., Mróz Z., FE investigations of the effect of fluctuating local tensile strength on coupled energetic-statistical size effect in concrete beams, ENGINEERING STRUCTURES, ISSN: 0141-0296, DOI: 10.1016/j.engstruct.2015.09.011, Vol.103, pp.239-259, 2015Abstract:The effect of fluctuating local tensile strength on a coupled energetic–statistical size effect in plain concrete beams under bending was numerically investigated. First, the influence of varying autocorrelation length of the random field describing a spatial variation of local tensile strength was studied. Next, the influence of the coefficient of variation of local tensile strength was analyzed. The numerical FE investigations were performed for unnotched concrete beams of similar geometry under quasi-static three point bending within elasto-plastic model assumptions, accounting for non-local softening. The FE analyses were carried out for four different beam sizes. In the calculations, the tensile strength took the form of spatially correlated random field described by a Gaussian distribution.Keywords:Autocorrelation length, Concrete beam, Elasto-plasticity, Non-local softening, Random field, Size effect, Strain localization, Tensile strength 35p. 8 Páczelt I., Mróz Z., Analysis of thermo-mechanical wear problems for reciprocal punch sliding, Advances in Engineering Software, ISSN: 0965-9978, DOI: 10.1016/j.advengsoft.2014.09.012, Vol.80, pp.139-155, 2015Páczelt I., Mróz Z., Analysis of thermo-mechanical wear problems for reciprocal punch sliding, Advances in Engineering Software, ISSN: 0965-9978, DOI: 10.1016/j.advengsoft.2014.09.012, Vol.80, pp.139-155, 2015Abstract:The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. In the case of a punch sliding on a substrate the transient process tends to a steady state for which the fixed contact stress and strain distribution develops in the contact zone. This state usually corresponds to a minimum of the wear dissipation power. The optimality conditions of the wear dissipation functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. The present paper is aimed to extend the previous analyses [1], [2], [3], [4] and [5] of steady state conditions to cases of periodic sliding of punch, assuming cyclic steady state conditions for both mechanical and thermal fields.Keywords:Contact optimization problems, Monotonic and periodic sliding wear, Heat generation, Steady wear state, Shape evolution, p-version of the finite element method 30p. 9 Mróz Z., Mróz K.P., Analysis of delamination and damage growth in joined bi-layer systems, Geomechanics for Energy and the Environment, ISSN: 2352-3808, DOI: 10.1016/j.gete.2015.10.001, Vol.4, No. Special Issue: 70th Anniversary of Professor Tomasz Hueckel, pp.4-28, 2015Mróz Z., Mróz K.P., Analysis of delamination and damage growth in joined bi-layer systems, Geomechanics for Energy and the Environment, ISSN: 2352-3808, DOI: 10.1016/j.gete.2015.10.001, Vol.4, No. Special Issue: 70th Anniversary of Professor Tomasz Hueckel, pp.4-28, 2015Abstract:The analysis of mechanical response of joined bi- or multi-layer systems is a typical problem for both geomechanics and composite technology. The elastic or visco-elastic layers interact through joining interfaces transferring stress state between layers and assuring structure integrity. The typical damage modes are related to progressive delamination at bonding interfaces, affected by distributed layer cracking. The present work is aimed to provide an analytical study of the stress state in a bi-layer system and of the progressive delamination process. The cohesive zone model is applied to simulate the interface response with shear stresses related to displacement discontinuities and to the specific fracture energies in shear mode. The following specific issues are discussed: delamination mode growth with the related critical and post-critical response of evaluation length of the process zone, scale effect of the critical stress. The analysis results can be applied to clarify the effect of material parameters on the damage process and to discuss experimental testing of epoxy joined ceramic elements, with specification of the connection strength, related to both the critical interface stress and the specific fracture energy.Keywords:Delamination, Cohesive zone, Shear lag, Damage process 10 Páczelt I., Mróz Z., Baksa A., Analysis of steady wear processes for periodic sliding, Journal of Computational and Applied Mechanics, ISSN: 1586-2070, Vol.10, No.2, pp.231-268, 2015Páczelt I., Mróz Z., Baksa A., Analysis of steady wear processes for periodic sliding, Journal of Computational and Applied Mechanics, ISSN: 1586-2070, Vol.10, No.2, pp.231-268, 2015Abstract:The relative sliding motion of two elastic bodies in contact induces the wear process and contact shape evolution. The transient process at the constant relative velocity between the bodies tends to a steady state occurring at fixed contact stress and strain distribution. This state corresponds to a minimum of the wear dissipation power. The optimality conditions of the functional provide a contact stress distribution and a wear rate compatible with the rigid body punch motion. The present paper is devoted to the analysis of wear processes occurring for periodic sliding of contacting bodies, assuming cyclic steady state conditions for mechanical fields. From the condition of the rigid body wear velocity a formula for summarized contact pressure in the periodic steady state is derived. The optimization problem is formulated for calculation of the contact surface shape induced by wear in the steady periodic state. Keywords:steady wear process, periodic sliding, unilateral contact, p-version of finite element method, shape optimization 11 Syroka-Korol E., Tejchman J., Mróz Z., FE analysis of size effects in reinforced concrete beams without shear reinforcement based on stochastic elasto-plasticity with non-local softening, FINITE ELEMENTS IN ANALYSIS AND DESIGN, ISSN: 0168-874X, DOI: 10.1016/j.finel.2014.05.005, Vol.88, pp.25-41, 2014Syroka-Korol E., Tejchman J., Mróz Z., FE analysis of size effects in reinforced concrete beams without shear reinforcement based on stochastic elasto-plasticity with non-local softening, FINITE ELEMENTS IN ANALYSIS AND DESIGN, ISSN: 0168-874X, DOI: 10.1016/j.finel.2014.05.005, Vol.88, pp.25-41, 2014Abstract:The paper presents results of FE analysis of mechanical size effects in longitudinally reinforced concrete slender beams without shear reinforcement failing in shear mode. The simulations were performed under plane stress conditions for three beams of different sizes and a fixed shape (height/length ratio). The attention was focused on deterministic and statistical size effects related to the nominal beam shear strength. Concrete was assumed as an isotropic elasto-plastic material exhibiting non-local softening. The bond strength between concrete and reinforcement was assumed to depend on interface slip with both stable and softening responses. Statistical simulations were performed for spatially correlated Gaussian random fields of tensile strength using a stratified sampling reduction method. The FE numerical results were compared with the respective own experimental test results.Keywords:Elasto-plasticity, Non-local softening, Random fields, Reinforced concrete beams, Size effect, Strain localization 35p. 12 Balevičius R., Mróz Z., A finite sliding model of two identical spheres under displacement and force control. Part II: dynamic analysis, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/s00707-013-1016-x, Vol.225, pp.1735-1759, 2014Balevičius R., Mróz Z., A finite sliding model of two identical spheres under displacement and force control. Part II: dynamic analysis, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/s00707-013-1016-x, Vol.225, pp.1735-1759, 2014Abstract:In Part I of the present study, the static analysis for the sliding of two identical spheres under displacement and force control was carried out. For linear and circular sliding trajectories, the contact traction evolution was analytically specified for both monotonic and reciprocal sliding regimes. Similarly, for the specified gravity loading, the driving force evolution and the sliding path were also determined. In the present Part II of the analysis, the dynamic response for the same sliding modes is presented. The contact traction and velocity evolutions are considered in detail. The analytical formulae are proposed for prediction of the tangential restitution coefficient, critical velocity, and time of contact for the displacement and load-controlled motions. The effects of loading and reloading in reciprocal sliding are also considered with account for the slip and sliding regimes. The generated results have practical aspects and can be implemented in modeling of the asperity and rough surface interaction, wear analysis and also in the development of the numerical discrete element method. 25p. 13 Páczelt I., Mróz Z., On steady wear states for monotonic relative sliding of contacting bodies, KEY ENGINEERING MATERIALS, ISSN: 1662-9795, DOI: 10.4028/www.scientific.net/KEM.618.49, Vol.618, pp.49-71, 2014Páczelt I., Mróz Z., On steady wear states for monotonic relative sliding of contacting bodies, KEY ENGINEERING MATERIALS, ISSN: 1662-9795, DOI: 10.4028/www.scientific.net/KEM.618.49, Vol.618, pp.49-71, 2014Abstract:The paper presents a synthetic review of recent research carried out by the writers [1-6, 7-9] on contact shape optimization coupled with wear and on the steady wear regimes reached in the transient wear process. It was shown that these regimes can also be specified from the optimality conditions. In the analysis several classes of shape optimization problems were considered, namely minimization of wear volume rate, friction dissipation power or wear dissipation power. It was demonstrated that the contact shape evolution tends to steady or quasi-steady states satisfying the minimum principle of the wear dissipation power, resulting in the coaxiality rule requiring the wear rate vector to be collinear with the rigid body wear velocity vector. The application of steady state wear rules in specification of contact states for selected problems is discussed in the paper. The extension of method is presented for the case of multi-zone contact problems for which both transient and steady states have been analyzed.Keywords:Contact Optimization, P-Version of Finite Element Method, Steady Wear State, Variational Principles 8p. 14 Syroka-Korol E., Tejchman J., Mróz Z., FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elasto-plasticity and non-local softening, ENGINEERING STRUCTURES, ISSN: 0141-0296, DOI: 10.1016/j.engstruct.2012.09.013, Vol.48, pp.205-219, 2013Syroka-Korol E., Tejchman J., Mróz Z., FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elasto-plasticity and non-local softening, ENGINEERING STRUCTURES, ISSN: 0141-0296, DOI: 10.1016/j.engstruct.2012.09.013, Vol.48, pp.205-219, 2013Abstract:The numerical FE investigations of a deterministic and statistical size effect in unnotched concrete beams of similar geometry under quasi-static three point bending were performed within elasto-plasticity with non-local softening. The FE analyses were carried out with four different beam sizes. Deterministic calculations were performed with the uniform distribution of a tensile strength. In turn, in statistical calculations, the tensile strength took the form of spatially correlated random fields described by a truncated Gaussian distribution. In order to reduce the number of statistical realizations without losing the calculation correctness, Latin hypercube sampling was applied. The numerical outcomes showed a strong coupled deterministic and stochastic size effect which was compared with the size effect laws by Bazant and by Carpinteri.Keywords:Concrete beam, Elasto-plasticity, Latin hypercube sampling, Non-local softening, Stochastic fields, Size effect, Strain localization, Tensile strength 40p. 15 Balevičius R., Mróz Z., A finite sliding model of two identical spheres under displacement and force control ‒ part I: static analysis, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/s00707-013-0839-9, Vol.224, No.8, pp.1659-1684, 2013Balevičius R., Mróz Z., A finite sliding model of two identical spheres under displacement and force control ‒ part I: static analysis, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/s00707-013-0839-9, Vol.224, No.8, pp.1659-1684, 2013Abstract:A simplified analytical model of tangential contact engagement, sliding and separation of two elastic, identical spheres is developed assuming the kinematically induced sphere motion trajectory or load controlled sliding motion. The evaluation of driving force during contact sliding motion is determined for both monotonic and reciprocal sliding motion. The analytical formulae and diagrams of driving force versus sliding path are specified for linear and circular paths. The sliding trajectories are also determined for the load controlled programs. The results presented can be applied in the experimental testing of frictional response of contacting bodies, in a wear study of rough surfaces or in the contact interaction analysis of granular material during flow. The results can also be relevant for the development of the discrete element method widely applied in simulation of granular material flow, where the sliding regime conditions prevail in grain contact interaction. 25p. 16 Mróz Z., Yanakieva A., Valeva V., Ivanova J., Analytical pullout analysis for carbon nanotube-cement composites under static loading, Comptes rendus de l'Académie bulgare des Sciences, ISSN: 1310-1331, Vol.66, No.3, pp.431-438, 2013Mróz Z., Yanakieva A., Valeva V., Ivanova J., Analytical pullout analysis for carbon nanotube-cement composites under static loading, Comptes rendus de l'Académie bulgare des Sciences, ISSN: 1310-1331, Vol.66, No.3, pp.431-438, 2013Abstract:The paper presents analytical pullout analysis for Carbon nanotube-cement composite based on Shear-lag assumptions. The composites under study are cement matrix composites reinforced by means of unidirectional Carbon nanotubes (CNT). The interface is assumed to be a material line with constitutive behaviour characterized by a relation between sliding stress and relative sliding displacement. Frictional sliding at the interface region is described by three different interface models: (i) Constant-τ model; (ii) Linear slip-hardening model and, (iii) Linear slip-softening model. The pullout analysis is performed considering static loading. The numerical examples are performed for concrete geometrical and material characteristics for CNT/cement composite. The obtained results are illustrated by figures and discussed.Keywords:Carbon nanotube cement reinforced composites, Interface sliding models, Pullout analysis, Shear-lag model, Static loading 15p. 17 Maciejewski G., Mróz Z., Optimization of functionally gradient materials in valve design under cyclic thermal and mechanical loading, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.20, No.2, pp.99-112, 2013Maciejewski G., Mróz Z., Optimization of functionally gradient materials in valve design under cyclic thermal and mechanical loading, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.20, No.2, pp.99-112, 2013Abstract:The robust and simple optimization method of functionally graded material (FGM) for combined cyclic thermal and mechanical loading with application to valve de sign is proposed. The optimization procedure starts from the homogeneous ceramic material distribution and after thermomechanical analysis of the whole process, the new distribution of material is determined by reducing concentration of the ceramic phase at places of high tensile stresses and by increasing ceramic contents at places of high effective stresses. The optimal distribution of ceramic phase is found through iterations. We have shown the numerical example of the proposed method for optimization of a composite exhaust valve of combustion engine. The example illustrates the optimal density distribution of ceramic phase of Al 2 O 3 within NiAl matrix. In the design study we have used the transient analysis of stress and temperature fields. The proposed method shares merits of standard optimization and topology optimization, it allows for creating one phase of material inside the other. It can be especially useful to problems of structural elements subjected to thermomechanical loading histories.Keywords:thermomechanical analysis, high frequency cyclic loading, coating, design, FGM, optimization 4p. 18 Balevičius R., Mróz Z., The Combined Slip and Finite Sliding Models in a Frictional Contact Interaction of Two Spherical Particles, Procedia Engineering, ISSN: 1877-7058, DOI: 10.1016/j.proeng.2013.04.024, Vol.57, pp.167-174, 2013Balevičius R., Mróz Z., The Combined Slip and Finite Sliding Models in a Frictional Contact Interaction of Two Spherical Particles, Procedia Engineering, ISSN: 1877-7058, DOI: 10.1016/j.proeng.2013.04.024, Vol.57, pp.167-174, 2013Abstract:A simplified analytical modelling of tangential contact interaction of two elastic spheres was presented accounting for the kinematically induced sphere trajectory or a load controlled sliding process. The evolution of driving force in combined slip and finite sliding interaction was considered for both monotonic and reciprocal sliding motion. The analytical formulae and diagrams for the evolution of driving force along the sliding path in terms of the main contact geometry parameters were specified. The sliding trajectories and contact tractions were also determined. The analytical formulae were briefly presented for prediction of the tangential restitution coefficient and time of contact. The results presented can be applied in the experimental testing of frictional response of contacting bodies, wear studies of rough surfaces or in the contact interaction analysis of granular material during flow. The results can also be relevant for development of the discrete element method widely applied in simulation of granular material flow, where the sliding regime conditions prevail in intergranular contact interactions.Keywords:sphere-sphere contact, slip and finite sliding, displacement and force control, monotonic and reciprocal sliding, traction and velocity evolution, coefficient of restitution, time period of contact interaction 19 Páczelt I., Mróz Z., Solution of wear problems for monotonic and periodic sliding with p-version of finite element method, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/j.cma.2012.02.012, Vol.249-252, pp.75-103, 2012Páczelt I., Mróz Z., Solution of wear problems for monotonic and periodic sliding with p-version of finite element method, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/j.cma.2012.02.012, Vol.249-252, pp.75-103, 2012Abstract:The relative sliding motion of two elastic bodies in contact under compressive tractions induces wear process and contact shape evolution. The transient process tends to a steady state at fixed contact stress and strain distribution. This state was assumed to correspond to the minimum of the wear dissipation power. The stationary condition of the response functional then provides the contact pressure distribution. The present paper is aimed at extending to results of previous analyses [1], [2], [3], [4] and [5] of steady state conditions to cases of periodic sliding of contacting bodies, assuming the existence of cyclic steady state conditions. The wear dissipation in the steady cyclic period is then minimized with respect to the contact pressure distribution. The solutions of several cases of wear processes induced by translational and rotational sliding illustrate the applicability of the proposed variational method.Keywords:Contact problems, Sliding wear, Steady-state, Periodic sliding, Optimal contact surface, p-Version of finite elements 40p. 20 Páczelt I., Kucharski S., Mróz Z., The experimental and numerical analysis of quasi-steady wear processes for a sliding spherical indenter, WEAR, ISSN: 0043-1648, DOI: 10.1016/j.wear.2011.08.026, Vol.274-275, pp.127-148, 2012Páczelt I., Kucharski S., Mróz Z., The experimental and numerical analysis of quasi-steady wear processes for a sliding spherical indenter, WEAR, ISSN: 0043-1648, DOI: 10.1016/j.wear.2011.08.026, Vol.274-275, pp.127-148, 2012Abstract:The wear process on a frictional interface in a relative sliding motion of a punch on a substrate induces shape evolution of contact interface. For fixed contact zone the process tends to a steady state with fixed contact stress and strain distribution. Such steady state wear regimes were analyzed in the previous papers [1], [2], [3], [4] and [5] by applying the principle of minimum wear dissipation rate. However, when the contact zone evolves in time due to wear process, as in the case of sliding spherical indenter, a quasi-steady state is reached with stress intensity dependent on the contact size parameter. On the other hand, the contact pressure distribution satisfies the condition of steady state. The simplified numerical analysis of wear process is presented by applying the quasi-steady conditions. The numerical predictions are confronted with experimental test results for two specific cases of soft and hard substrates. The quantitative specification of wear parameters is provided, first assuming constant values throughout the whole wear process, next assuming linearly or exponentially varying during the initial period and tending to constant values.Keywords:Spherical indenter, Sliding wear, Contact zone evolution, Wear parameters, Experimental data, Numerical simulation 40p. 21 Bojczuk D., Mróz Z., Topological sensitivity derivative with respect to area, shape and orientation of an elliptic hole in a plate, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-011-0710-3, Vol.45, pp.153-169, 2012Bojczuk D., Mróz Z., Topological sensitivity derivative with respect to area, shape and orientation of an elliptic hole in a plate, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-011-0710-3, Vol.45, pp.153-169, 2012Abstract:The topological sensitivity derivative of a functional expressed in terms of displacement, strain or stress fields and boundary tractions is derived for the case of an elliptical hole introduced in the plate. The derivative is specified with respect to the hole area, the length of ellipse axes and their orientation in terms of primary and adjoint state fields. The shape sensitivity derivative for a finite hole can be applied and the topological derivative with respect to the hole area is obtained in the limiting case. The transition to a plane crack occurs for vanishing length of minor axis and the topological derivative with respect to crack length is then derived from the general formulae. The results can be useful in optimal design procedures by selecting positions, shape and orientation of elliptical cutouts.Keywords:Topological sensitivity, Elliptical hole, Plate, Plane crack, Optimal design 35p. 22 Balevičius R., Sielamowicz I., Mróz Z., Kačianauskas R., Effect of rolling friction on wall pressure, discharge velocity and outﬂow of granular material from a ﬂat-bottomed bin, PARTICUOLOGY, ISSN: 1674-2001, DOI: 10.1016/j.partic.2012.07.002, Vol.10, pp.672-682, 2012Balevičius R., Sielamowicz I., Mróz Z., Kačianauskas R., Effect of rolling friction on wall pressure, discharge velocity and outﬂow of granular material from a ﬂat-bottomed bin, PARTICUOLOGY, ISSN: 1674-2001, DOI: 10.1016/j.partic.2012.07.002, Vol.10, pp.672-682, 2012Abstract:The present paper provides both experimental and DEM analyses of the filling and discharge of pea grains from a 3D flat-bottomed bin. In the DEM model, the fixed mean values of the experimentally determined single particle data, such as the particle density, Young's modulus, Poisson's ratio as well as the sliding and rolling friction coefficients were incorporated to analyse their effects on the macroscale indicators, such as the wall pressure, discharge velocities and material outflow parameters. The effect of rolling friction was studied based on the experimentally measured single particle rolling friction coefficient. This analysis is aimed at the quantitative prediction of flow parameters as related to the identification of material parameters.Keywords:Visco-elastic granular material, Discrete element method, Rolling friction, Wall pressure, Material velocity, Outflow mass, Outflow rate, Biosystems, Pea grains 30p. 23 Kozicki J., Tejchman J., Mróz Z., Effect of grain roughness on strength, volume changes, elastic and dissipated energies during quasi-static homogeneous triaxial compression using DEM, GRANULAR MATTER, ISSN: 1434-5021, DOI: 10.1007/s10035-012-0352-1, Vol.14, pp.457-468, 2012Kozicki J., Tejchman J., Mróz Z., Effect of grain roughness on strength, volume changes, elastic and dissipated energies during quasi-static homogeneous triaxial compression using DEM, GRANULAR MATTER, ISSN: 1434-5021, DOI: 10.1007/s10035-012-0352-1, Vol.14, pp.457-468, 2012Abstract:A quasi-static homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a three-dimensional DEM model. Grain roughness was modelled by means of symmetric clusters composed of rigid spheres imitating irregular particle shapes. The effect of grain roughness on shear strength, dilatancy, kinetic, elastic and dissipated energies was numerically analyzed. Some numerical results were compared with available experimental results.Keywords:Triaxial test, Granular material, Discrete element method, Grain roughness, Energy, Dissipation 30p. 24 Dems K., Mróz Z., Analysis and design of thermo-mechanical interfaces, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, DOI: 10.2478/v10175-012-0027-4, Vol.60, No.2, pp.205-213, 2012Dems K., Mróz Z., Analysis and design of thermo-mechanical interfaces, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, DOI: 10.2478/v10175-012-0027-4, Vol.60, No.2, pp.205-213, 2012Abstract:An elastic structure subjected to thermal and mechanical loading with prescribed external boundary and varying intern al interface is considered. The different thermal and mechanical nature of this interface is discussed, since the interface form and its properties affect strongly the structural response. The first-order sensitivities of an arbitrary thermal and mechanical behavioral functional with respect to shape and material properties of the interface are derived u sing the direct or adjoint approaches. Next the relevant optimality conditions are formulated. Some examples illustrate the applicability of proposed approach to control the structural response due to applied thermal and mechanical loads.Keywords:multiphase structures, sensitivity analysis, optimization, heat transfer, thermo-elasticity 30p. 25 Mróz Z., Bojczuk D., Shape and topology sensitivity analysis and its application to structural design, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/s00419-012-0672-y, Vol.82, pp.1541-1555, 2012Mróz Z., Bojczuk D., Shape and topology sensitivity analysis and its application to structural design, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/s00419-012-0672-y, Vol.82, pp.1541-1555, 2012Abstract:The incremental sensitivity analysis associated with variation of structure material parameters, shape or topology variation is generally discussed by analyzing the evolution of potential and complementary energies, or arbitrary functionals of state fields. The concept of configuration and sensitivity generalized forces is used in presenting the sensitivity derivatives. The general reciprocity relations are derived for the case of potential or complementary energy variations. The topology variations in bar structures related to introduction of elements and introduction of inclusions and voids in plates are discussed, and the sensitivity forces are derived.Keywords:Sensitivity analysis, Topological derivative, Structural design, Bar structures, Plates 20p. 26 Kucharski S., Mróz Z., Identification of wear process parameters in reciprocating ball-on-disc tests, TRIBOLOGY INTERNATIONAL, ISSN: 0301-679X, DOI: 10.1016/j.triboint.2010.10.010, Vol.44, pp.154-164, 2011Kucharski S., Mróz Z., Identification of wear process parameters in reciprocating ball-on-disc tests, TRIBOLOGY INTERNATIONAL, ISSN: 0301-679X, DOI: 10.1016/j.triboint.2010.10.010, Vol.44, pp.154-164, 2011Abstract:Wear test results are presented for a spherical indenter in reciprocal motion interacting with soft (aluminium alloy) and hard (construction steel) substrates. The aim of this paper is to provide evidence of the evolution of the contact zone, specification of wear scar depth and surface roughness in the contact zone. Numerical analysis of the interaction of the sliding sphere with the wear track provided contact zone dimensions, although these differed from the experimental data. The incremental wear factor is also introduced in the paper, while the formulae for the wear volume of the sphere recommended by ASTM have been improved.Keywords:Dry wear, Contact area, Wear factor, Finite element method 40p. 27 Páczelt I., Mróz Z., Numerical analysis of steady thermo-elastic wear regimes induced by translating and rotating punches, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2011.06.001, Vol.89, pp.2495-2521, 2011Páczelt I., Mróz Z., Numerical analysis of steady thermo-elastic wear regimes induced by translating and rotating punches, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2011.06.001, Vol.89, pp.2495-2521, 2011Abstract:The present work provides the analysis of coupled thermo-elastic steady wear regimes: wear analysis of a punch translating on an elastic strip and wear induced by a rotating punch on a toroidal surface. The contact pressure and temperature are specified from the stationary conditions of the wear dissipation power or from the contact-conformity-condition. The wear and friction parameters are assumed as fixed or temperature dependent. Three transverse friction models are discussed for wear debris motion. The analysis and results presented can be used in design of optimal contact shapes assuring the steady wear regimes throughout the whole contact operation period.Keywords:Contact problems, Sliding wear, Steady state, Thermal distortion, Optimal contact surface 35p. 28 Balevičius R., Sielamowicz I., Mróz Z., Kačianauskas R., Investigation of wall stress and outflow rate in a flat-bottomed bin: a comparison of the DEM model results with the experimental measurements, POWDER TECHNOLOGY, ISSN: 0032-5910, DOI: 10.1016/j.powtec.2011.08.042, Vol.214, pp.322-336, 2011Balevičius R., Sielamowicz I., Mróz Z., Kačianauskas R., Investigation of wall stress and outflow rate in a flat-bottomed bin: a comparison of the DEM model results with the experimental measurements, POWDER TECHNOLOGY, ISSN: 0032-5910, DOI: 10.1016/j.powtec.2011.08.042, Vol.214, pp.322-336, 2011Abstract:The present paper provides a discrete element method (DEM) analysis of the filling and discharge processes of granular material in a 3D flat-bottomed bin. A granular aggregate of nearly round particles (20,400 pea grains, 7.2–7.8 mm in diameter) is considered. The numerical results are compared with the experimental data. The DEM analysis provides an accurate prediction of wall stress distribution and the outflow rate of discharge throughout the bottom orifice. The stress distribution developed within the granular material after filling and during the discharge phase is considered, and the transition from the active to passive stress state is discussed. This analysis aims to quantitatively predict the flow parameters related to the careful identification of the material parameters. The investigation presented may be useful for the ongoing development of DEM.Keywords:Visco-elastic granular material, Discrete element method, Wall pressure, Granular material stress, Micro-properties, Bulk properties 35p. 29 Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Analysis and DEM simulation of granular material flow patterns in hopper models of different shapes, ADVANCED POWDER TECHNOLOGY, ISSN: 0921-8831, DOI: 10.1016/j.apt.2010.12.005, Vol.22, pp.226-235, 2011Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Analysis and DEM simulation of granular material flow patterns in hopper models of different shapes, ADVANCED POWDER TECHNOLOGY, ISSN: 0921-8831, DOI: 10.1016/j.apt.2010.12.005, Vol.22, pp.226-235, 2011Abstract:By using the discrete element method (DEM) a comparison and observations on material flow patterns in plane-wedged, space-wedged, and flat-bottomed hopper were accounted for. Numerical results obtained by combining data of individual particles, statistical processing of particle assemblies and evaluation of the field variables provided the essential characteristics for different regimes of the discharge flow (within steady or unsteady state of flow) and the differences in differently shaped hoppers due to different microscopic inter-particle friction. For validation of the performed simulations, velocity patterns developed in three-dimensional flat-bottomed hopper containing 20,400 pea grains were also analysed. To represent the continuum by avoiding the local effects produced by the individual grains, the simulation results were focused on the mean velocity distributions with data smoothening. The effect of rolling resistance on granular material flow was also considered.Keywords:DEM, Mass flow rate, Velocity distribution, Plane-wedged, Space-wedged, Flat-bottomed hoppers 25p. 30 Mróz Z., Páczelt I., Analysis of thermo-elastic wear problems, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2011.564026, Vol.34, pp.569-606, 2011Mróz Z., Páczelt I., Analysis of thermo-elastic wear problems, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2011.564026, Vol.34, pp.569-606, 2011Abstract:In the relative sliding motion of two elastic bodies on contact interfaces both frictional dissipation and wear process occur. The wear process induces shape evolution of contact surface and growth of contact zone. The temperature field is generated by external heat flow and by frictional dissipation on the contact surface. The wear and heat conduction processes are coupled and tend to their steady or quasi-steady states for which the stress and temperature fields are fixed on the translating contact zone and depend only on its size and shape parameters. The steady-state is characterized by the minimum of wear dissipation power for which the stationary conditions generate the contact pressure distribution. The related steady-state temperature field is next specified and the thermal distortion effect is analyzed. The contact shape attained in the steady wear state is optimal as it corresponds to minimal wear rate, and its form depends on both mechanical loading and temeperature field. Several specific examples are presented for translating and rotating punches. Keywords:Contact optimization, Heat generation, Minimum principle,p-version of finite element method, Sliding wear, Steady wear state, Thermo-elastic problem, Upwinding Petrov-Galerkin scheme 20p. 31 Ziętek G., Mróz Z., On the hardening rule for austenitic steels accounting for the strain induced martensitic transformation, INTERNATIONAL JOURNAL OF STRUCTURAL CHANGES IN SOLIDS – Mechanics and Applications, Vol.3, No.3, pp.21-34, 2011Ziętek G., Mróz Z., On the hardening rule for austenitic steels accounting for the strain induced martensitic transformation, INTERNATIONAL JOURNAL OF STRUCTURAL CHANGES IN SOLIDS – Mechanics and Applications, Vol.3, No.3, pp.21-34, 2011Abstract:The elasto-plastic hardening model for austenitic steels undergoing plastic strain induced martensitic transformation is presented with application to both monotonic and cyclic loading processes. The kinematic hardening rule is assumed and expressed in terms of the back stress Z composed of two portions X and X t, the first related to plastic strain, the other to phase transformation and volume fraction of martensite. The transformation process is assumed to be driven by the back stress difference X – Y, where Y is the transformation back stress related to growth of the martensitic phase. The non-linear coupling of hardening and phase transformation processes occurs due to interaction of back stresses X and X t. The thermodynamic framework is applied by introducing state variables and conjugate forces used in specifying the plastic flow and evolution rules. The model is applied to simulate cyclic hardening response for uniaxial tension-compression tests and for combined tension-torsion tests. The cyclic stress-strain curves for specified strain amplitudes are used in material parameter calibration.Keywords:plastic deformation, martensitic transformation, kinematic hardening, back stresses, cyclic deformation, increased hardening rates, decreased ratcheting strains 32 Dems K., Mróz Z., Damage identification using modal, static and thermographic analysis with additional control parameters, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2010.07.005, Vol.88, pp.1254-1264, 2010Dems K., Mróz Z., Damage identification using modal, static and thermographic analysis with additional control parameters, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2010.07.005, Vol.88, pp.1254-1264, 2010Abstract:The present paper provides the analysis of identification of damage or material parameters by using variation of modal characteristics (eigenvalues and eigenmodes), static or dynamic compliance and temperature fields. The distance norm between the measured and predicted by model data is assumed to depend also on an additional control parameter introduced in the system in order to increase sensitivity with respect to identified parameters. In the case of frame and plate structures such assisting control can be executed by additional supports, masses or loads introduced into a structure. In the case of thermal loading, the distribution of heat sources or boundary temperature may constitute control parameters. The proposed methodology is illustrated by analyzing identification of location and magnitude of damage in beams and plates by means of variation of free frequency spectrum and the related free vibration modes. Similarly for the thermal problem the heat flux distribution on the boundary is specified in order to increase the sensitivity of the assumed distance norm.Keywords:Damage identification, Modal analysis, Static, dynamic and thermal loads, Assisting control parameters 32p. 33 Mróz K.P., Mróz Z., On crack path evolution rules, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/j.engfracmech.2010.03.038, Vol.77, pp.1781-1807, 2010Mróz K.P., Mróz Z., On crack path evolution rules, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/j.engfracmech.2010.03.038, Vol.77, pp.1781-1807, 2010Abstract:The models of crack growth in mixed mode conditions are reviewed for the plane and three-dimensional (3D) states of stress. Both critical load value and crack path or surface growth are predicted by different criteria in terms of elastic singular stress states and T-stress component. Monotonic and cyclic loading induced crack growth is considered. The energy and critical plane criteria based on local or non-local measure of stress and strain are most useful in developing predictive crack growth simulation. The finite critical distance from the crack tip should be specified to provide averaged or local stress and strain states. The application of MK-criterion of crack growth expressed in terms of volumetric and deviatoric strain energies is presented for several specific cases of monotonic and cyclic loading. The concepts of smooth and rough crack surface are discussed with application to 3D crack surface growth.Keywords:Fracture criteria, T-stress, Fatigue crack growth, 3D crack, Smooth and rough cracks, Crack path, Critical plane, Non-local models 32p. 34 Páczelt I., Mróz Z., Variational approach to the analysis of steady state thermo-elastic wear regimes, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.2709, Vol.81, pp.728-760, 2010Páczelt I., Mróz Z., Variational approach to the analysis of steady state thermo-elastic wear regimes, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.2709, Vol.81, pp.728-760, 2010Abstract:A transient wear process on frictional interface of two thermo-elastic bodies in a relative steady sliding motion induces shape evolution of contact interface and tends to a steady state for which the wear process occurs at fixed contact stress and strain distribution. The temperature field generated by frictional and wear dissipation on the contact surface is assumed to reach a steady state. This state is assumed to correspond to minimum of the wear dissipation power and the temperature field corresponds to maximum of the heat entropy production. The stationarity conditions of the response functionals provide the contact pressure distribution and the corresponding temperature field. The present approach extends the authors previous analyses of optimal or steady-state contact shapes by accounting for coupled wear and thermal distortion effects. The wear rule is assumed as a non-linear relation of wear rate to shear stress and relative sliding velocity. The analysis of disk and drum brakes is presented with account for thermal distortion effect. It is shown that the contact shape in a steady thermo-elastic state essentially differs from that specified for mechanical loading with neglect of thermal effects. The thermal instability regimes are not considered in the paper. 32p. 35 Bojczuk D., Mróz Z., Topological sensitivity derivative and finite topology modifications: application to optimization of plates in bending, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-008-0333-5, Vol.39, pp.1-15, 2009Bojczuk D., Mróz Z., Topological sensitivity derivative and finite topology modifications: application to optimization of plates in bending, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-008-0333-5, Vol.39, pp.1-15, 2009Abstract:The concept of topological sensitivity derivative is introduced and applied to study the problem of optimal design of structures. It is assumed, that virtual topology variation is described by topological parameters. The topological derivative provides the gradients of objective functional and constraints with respect to these parameters. This derivative enables formulation of the conditions of topology transformation. In this paper formulas for the topological sensitivity derivative for bending plates are derived. Next, the topological derivative is used in the optimization process in order to formulate conditions of finite topology modifications and in order to localize positions of the modifications. In the case of plates they are related to introduction of holes and introduction of stiffeners. The theoretical considerations are illustrated by some numerical examples.Keywords:Topological sensitivity derivative, Finite topology modifications, Bending plates, Optimal topology and shape, Optimal layout of ribs 32p. 36 Páczelt I., Mróz Z., On the analysis of steady-state sliding wear processes, TRIBOLOGY INTERNATIONAL, ISSN: 0301-679X, DOI: 10.1016/j.triboint.2008.06.007, Vol.42, No.2, pp.275-283, 2009Páczelt I., Mróz Z., On the analysis of steady-state sliding wear processes, TRIBOLOGY INTERNATIONAL, ISSN: 0301-679X, DOI: 10.1016/j.triboint.2008.06.007, Vol.42, No.2, pp.275-283, 2009Abstract:The transient wear process on the frictional interface of two elastic bodies in relative steady sliding motion induces shape evolution of the contact interface and tends to a steady state in which the wear develops at constant contact stress and strain distribution. Such a steady state may be attained experimentally or in numerical analysis by integrating the wear rate in the transient wear period. An alternative method of analysis was proposed in previous papers [Páczelt I, Mróz Z. On optimal contact shapes generated by wear. Int J Numer Methods Eng 2005;63:1310–47; Páczelt I, Mróz Z. Optimal shapes of contact interfaces due to sliding wear in the steady relative motion. Int J Solids Struct 2007;44:895–925] by applying a variational procedure and minimizing a response functional corresponding to the wear-dissipation power. The present paper provides an extension of this approach and new applications to the analysis of steady states in disk and drum brakes. The wear rule is assumed as a non-linear relation of wear rate to shear stress and relative sliding velocity. The specification of steady wear states is of engineering importance as it allows for optimal shape design of contacting interfaces in order to avoid the transient run-in periods. The extension to cyclic translation cases can be generated by considering steady cyclic states of wear processes.Keywords:Contact problems, Sliding wear, Steady-state, Variational principle, Optimal contact surface 32p. 37 Mróz Z., Janusz Klepaczko remembered, INTERNATIONAL JOURNAL OF IMPACT ENGINEERING, ISSN: 0734-743X, DOI: 10.1016/j.ijimpeng.2009.02.003, Vol.36, No.8, pp.994-994, 2009 38 Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Discrete particle investigation of friction effect in filling and unsteady/steady discharge in three-dimensional wedge shaped hopper, POWDER TECHNOLOGY, ISSN: 0032-5910, DOI: 10.1016/j.powtec.2008.02.006, Vol.187, No.2, pp.159-174, 2008Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Discrete particle investigation of friction effect in filling and unsteady/steady discharge in three-dimensional wedge shaped hopper, POWDER TECHNOLOGY, ISSN: 0032-5910, DOI: 10.1016/j.powtec.2008.02.006, Vol.187, No.2, pp.159-174, 2008Abstract:The friction effect in filling and unsteady/steady discharge of three-dimensional wedge-shaped hopper was considered numerically by the discrete element method. The presented model is based on contact mechanics of a single spherical particle involving Hooke's law of spring interaction, static and dynamic friction as well as viscous damping forces. The hopper filling process en masse was performed while the modeling of uncontrolled and controlled discharge was simulated. The evolution of the kinetic energy of filling, the distribution of stresses within granular material and stresses acting on the walls, as well as the change in fields of material porosity were investigated at the stages of filling and discharge of the hopper. The variation of flow velocities, the discharged mass fractions as well as discharge fraction rates were analyzed. The friction effect was analyzed by varying inter-particle friction coefficient over the range of 0–0.6. A comparison of the numerical results with available continuum-based predictions was also presented.Keywords:Visco-elastic granular material, 3D wedge-shaped hopper, Discrete element method, Wall pressure, Granular stresses, Fraction discharged, Bulk porosity 39 Maciejewski J., Mróz Z., An upper-bound analysis of axisymmetric extrusion assisted by cyclic torsion, JOURNAL OF MATERIALS PROCESSING TECHNOLOGY, ISSN: 0924-0136, DOI: 10.1016/j.jmatprotec.2007.12.061, Vol.206, pp.333-344, 2008Maciejewski J., Mróz Z., An upper-bound analysis of axisymmetric extrusion assisted by cyclic torsion, JOURNAL OF MATERIALS PROCESSING TECHNOLOGY, ISSN: 0924-0136, DOI: 10.1016/j.jmatprotec.2007.12.061, Vol.206, pp.333-344, 2008Abstract:Technological metal forming processes of extrusion, forging and rolling with imposed cyclic torsion or shear deformation are of engineering interest in view of their advantages with respect to monotonic loading processes. The present work is aimed at the analysis of an axisymmetric extrusion process assisted by cyclic torsion, which can be induced by a cyclically rotating die with a specified rotation amplitude and frequency. The material is assumed to be rigid-perfectly plastic and the upper-bound analysis for a kinematically admissible flow field is presented. The field parameters are specified from the condition of minimum plastic dissipation. The evolution of the extrusion force and torsional moment is studied and the corresponding plastic flow field is specified, with process control parameters such as the ratio of extrusion and rotation rates, and the amplitude of die rotation. For increasing rotation frequency, it is shown that localization of plastic flow occurs in the bottom zone close to the rotating die. The analysis allows for specification of process control parameters and their relation to extrusion force, torsional moment, and the associated plastic dissipation for varying reduction ratios.Keywords:Extrusion, Cyclic torsion, KOBO method, Upper-bound analysis, Process control parameters 40 Raniecki B., Mróz Z., Yield or martensitic phase transformation conditions and dissipation functions for isotropic, pressure-insensitive alloys exhibiting SD effect, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/s00707-007-0544-7, Vol.195, pp.81-102, 2008Raniecki B., Mróz Z., Yield or martensitic phase transformation conditions and dissipation functions for isotropic, pressure-insensitive alloys exhibiting SD effect, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/s00707-007-0544-7, Vol.195, pp.81-102, 2008Abstract:A class of nonsingular yield conditions depending on three parameters is analyzed for isotropic materials exhibiting strength differential effect and pressure insensitivity. The yield condition can then be expressed in terms of the second and third stress deviator invariants. The convexity requirement is considered and the constraints imposed on the material parameters are discussed in detail. The dual dissipation function is derived in the analytical form. The condition can be applied in the analysis of high strength alloys (such as Inconnel 718) or of shape memory alloys (such as NiTi, NiAl, CuZnGa, or CuAlNi) in order to specify the onset of yield, or of martensitic or austenitic transformation. The conditions can easily be generalized to account for mixed hardening and back stress anisotropy. Some experimental data are provided to verify the proposed conditions. 41 Wilczyński B., Mróz Z., Optimal design of machine components using notch correction and plasticity models, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2006.08.092, Vol.85, pp.1382-1398, 2007Wilczyński B., Mróz Z., Optimal design of machine components using notch correction and plasticity models, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2006.08.092, Vol.85, pp.1382-1398, 2007Abstract:Shape optimization computational technology is used in order to maximize life time of notched machine/structural components in low cycle fatigue regime. The present approach is composed of three steps: (i) stress–strain calculation using notch correction and plasticity models, (ii) estimation of critical plane to asses fatigue lives, (iii) formulation of the optimization problem with constraint set on the number of cycles corresponding to crack initiation. The optimal design procedure is a combination of the computer aided geometrical design mathematical methods for the shape definition, the boundary element method used for analysis of the response quantities, assisted by the sequential linear programming method with move limits. Numerical examples display significant increase in the number of cycles corresponding to crack initiation phase in comparison to traditional (regular) notch shapes.Keywords:Low cycle fatigue, Notch correction, Plasticity models, Fatigue life prediction, Life time maximization, Shape optimization 42 Kucharski S., Mróz Z., Identification of yield stress and plastic hardening parameters from a spherical indentation test, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/j.ijmecsci.2007.03.013, Vol.49, No.11, pp.1238-1250, 2007Kucharski S., Mróz Z., Identification of yield stress and plastic hardening parameters from a spherical indentation test, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/j.ijmecsci.2007.03.013, Vol.49, No.11, pp.1238-1250, 2007Abstract:Assuming plastic hardening of metals are specified by the stress–strain curve in the form View the MathML sourceσ=σ0+kεpm, the material parameters σ0, k and m are identified from spherical indentation tests by measuring compliance moduli in loading and unloading of the load–penetration curve. The curve P(hp) is analytically described by a two term expression, each with different exponents. Here, εp and hp denote the plastic strain and permanent penetration. The proposed identification method is illustrated by specific examples including numerical and physical identification tests.Keywords:Spherical indentation test, Identification, Finite element modelling, Elasto-plastic material properties 43 Páczelt I., Mróz Z., Optimal shapes of contact interfaces due to sliding wear in the steady relative motion, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/j.ijsolstr.2006.05.027, Vol.44, No.3-4, pp.895-925, 2007Páczelt I., Mróz Z., Optimal shapes of contact interfaces due to sliding wear in the steady relative motion, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/j.ijsolstr.2006.05.027, Vol.44, No.3-4, pp.895-925, 2007Abstract:The transient wear process at contact frictional interface of two elastic bodies in relative steady motion induces evolution of shape of the interface. A steady wear state may be reached with uniform wear rate and fixed contact surface shape. In this paper, the optimal contact shape is studied by formulating several classes of shape optimization problems, namely minimization of generalized wear volume rate, friction dissipation power and wear dissipation rate occurring in two bodies. The wear rule was assumed as a nonlinear dependence of wear rate on friction traction and relative sliding velocity, similar to the Archard rule. The wear parameters of two bodies may be different. It was demonstrated that different optimal contact shapes are generated depending on objective functional and wear parameters. When the uniform wear rate is generated at contact sliding surfaces, the steady state is reached. It was shown that in the steady state the wear parameters of two bodies cannot be independent of each other. The solution of nonlinear programming problem was provided by the iterative numerical procedure. It was assumed that the relative sliding velocity between contacting bodies results from translation and rotation of two bodies. In general, both regular and singular regimes of wear rate and pressure distribution may occur. The illustrative examples of drum brake, translating punch and rotating annular punch (disc brake) provide the distribution of contact pressure and wear rate for regular and singular cases associated with the optimality conditions. It is shown that minimization of the generalized wear dissipation rate provides solutions assuring existence of steady wear states.Keywords:Sliding wear, Contact optimization, Steady wear state, p-Version of finite element method 44 Białas M., Mróz Z., An energy model of segmentation cracking of thin films, MECHANICS OF MATERIALS, ISSN: 0167-6636, DOI: 10.1016/j.mechmat.2007.02.004, Vol.39, No.9, pp.845-864, 2007Białas M., Mróz Z., An energy model of segmentation cracking of thin films, MECHANICS OF MATERIALS, ISSN: 0167-6636, DOI: 10.1016/j.mechmat.2007.02.004, Vol.39, No.9, pp.845-864, 2007Abstract:On the basis of analytical modelling of delamination of a thin film on a stretched substrate an energy model of film segmentation cracking has been formulated. The model focuses on a topological transformation between an intact and a damaged structure, rather than on a constitutive modelling of fracture itself. An energy transition condition should be satisfied in order for cracks to occur. The model provides a unique solution in the number of cracks for given material parameters. It has been validated by measuring the fracture energy of a silicon oxide thin film deposited on a poly(ethylene terephthalate) (PET) substrate, where a constant value of plastic shear stress at the film/substrate interface can be assumed.Keywords:Segmentation cracking, Delamination, Fracture energy, Oxide coating 45 Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Microscopic and macroscopic analysis of granular material behaviour in 3D flat-bottomed hopper by the discrete element methody, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.59, pp.231-257, 2007Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Microscopic and macroscopic analysis of granular material behaviour in 3D flat-bottomed hopper by the discrete element methody, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.59, pp.231-257, 2007Abstract:The paper presents the application of the discrete element method to modelling of granular material filling and discharge in 3D flat-bottomed hopper. A mathematical model, as well as the developed software code, operates with spherical visco-elastic non-cohesive frictional particles. The evolution of granular flow, internal forces and densification (rarefaction) are characterized by macroscopic parameters such as the discharge rates, the porosity fields and the wall pressures, as well as by microscopic evaluations in terms of coordination number, velocity patter ns and inter-particle contact forces. It was shown that qualitative characterization of flow may be done even by relatively rough models with small number of particles, which required to be increased, however, for more precise description of the localize d phenomena. Unsatisfactory evaluation of the stress peak during discharge is p resented as an illustrative example. The main focus of the paper is the analysis of particle friction effect and the consistency of micro and macro-phenomena in the time-dependent flow process. Keywords:discrete element method, spherical particles, visco-elastic granular material, three-dimensional flat bottomed hopper 46 Mróz Z., Ziętek G., Modeling of cyclic hardening of metals coupled with martensitic transformation, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.59, No.1, pp.3-20, 2007Mróz Z., Ziętek G., Modeling of cyclic hardening of metals coupled with martensitic transformation, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.59, No.1, pp.3-20, 2007Abstract:The work presents an elasto-plastic material model with mixed hardening taking into account martensitic transformation. Modification of the kinematic hardening rule is proposed by relating back stress to the generalized thermodynamic force by a nonlinear function dependent on the fraction of martensite. The martensitic evolution is expressed in terms of isotropic hardening parameter by introducing proper free energy related force. The proposed model has been applied to predict hysteretic response for cyclic tension and compression tests for austenitic steel. 47 Kowalczyk-Gajewska K., Mróz Z., Pęcherski R.B., Micromechanical modelling of polycrystalline materials under non-proportional deformation paths, ARCHIVES OF METALLURGY AND MATERIALS, ISSN: 1733-3490, Vol.52, pp.181-192, 2007Kowalczyk-Gajewska K., Mróz Z., Pęcherski R.B., Micromechanical modelling of polycrystalline materials under non-proportional deformation paths, ARCHIVES OF METALLURGY AND MATERIALS, ISSN: 1733-3490, Vol.52, pp.181-192, 2007Abstract:The rigid-plastic crystal plasticity model with single yield surface of 2n-degree is applied to simulate the polycrystalline behaviour and the crystallographic texture development under non-proportional deformation paths. The role of two controlling parameters: the amplitude and frequency for the processes of tension or compression assisted by cyclic torsion of thin-walled tubes made of copper is analysed. The effect of micro-shear bands on the reduction of global hardening rate is described by means of the contribution function of shear banding in the rate of plastic deformation. The conclusions drawn from the study can find also application in the extension of the analysis for high strength and hard deformable materials.Keywords:micromechanics, modelling of materials, rigid-plastic solids, crystal plasticity, texture, cyclic torsion, non-proportional deformation path, micro-shear bands 48 Maciejewski J., Mróz Z., Analiza procesu wyciskania metali wspieranego deformacją cykliczną, RUDY I METALE NIEŻELAZNE, ISSN: 0035-9696, Vol.11, pp.668-677, 2007Maciejewski J., Mróz Z., Analiza procesu wyciskania metali wspieranego deformacją cykliczną, RUDY I METALE NIEŻELAZNE, ISSN: 0035-9696, Vol.11, pp.668-677, 2007Abstract:Przedstawiono analizę procesu osiowosymetrycznego wyciskania metali przy nałożeniu cyklicznego skręcania wywoływa-nego matrycą ( metoda KOBO, [1÷4]). Założono uproszczony model sztywno-plastycznego materiału bez wzmocnienia i ki-nematycznie dopuszczalny mechanizm płynięcia. Z warunku równości mocy dyssypacji plastycznej i mocy sił zewnętrznych (siła osiowa i moment skręcający) określono wartość [...] 49 Feng Z.-Q., Hjiaj M., de Saxcé G., Mróz Z., Effect of frictional anisotropy on the quasistatic motion of a deformable solid sliding on a planar surface, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-005-0674-5, Vol.37, pp.349-361, 2006Feng Z.-Q., Hjiaj M., de Saxcé G., Mróz Z., Effect of frictional anisotropy on the quasistatic motion of a deformable solid sliding on a planar surface, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-005-0674-5, Vol.37, pp.349-361, 2006Abstract:In this paper, the motion of a deformable body sliding on a half-plane is considered. The solid undergoes large displacements but small strains. An orthotropic friction model described by an elliptic cone is considered. This model allows to describe the sliding-direction dependence of the frictional behavior observed in experience. The algorithm used to solve the problem is based on a weak variational statement of the frictional contact law. The Uzawa algorithm is used to solve the discrete problem. The corresponding algorithm is robust and can deal with large sliding increments. The study shows that frictional properties can influence significantly the trajectory of a deformable body sliding on a frictional surface.Keywords:Elliptic friction criterion, Large sliding, Variational formulation, Uzawa algorithm 50 Białas M., Mróz Z., Crack patterns in thin layers under temperature loading. Part I. Monotonic loading, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/j.engfracmech.2005.10.012, Vol.73, pp.917-938, 2006Białas M., Mróz Z., Crack patterns in thin layers under temperature loading. Part I. Monotonic loading, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/j.engfracmech.2005.10.012, Vol.73, pp.917-938, 2006Abstract:The analysis of cracking and delamination of a plate bonded to a substrate is presented in the paper. The plate is subjected to a monotonic temperature loading. Several types of interface constitutive laws are used in order to obtain analytical solutions specifying the maximum number of plate fragments and the description of fragmentation process. The segmentation cracking model is further used to measure the ultimate shear strength of a thin film–substrate interface.Keywords:Cohesive zone modelling, Segmentation cracking, Delamination, Temperature loading 51 Białas M., Mróz Z., Crack patterns in thin layers under temperature loading. Part II. Cyclic loading, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/j.engfracmech.2005.10.013, Vol.73, pp.939-952, 2006Białas M., Mróz Z., Crack patterns in thin layers under temperature loading. Part II. Cyclic loading, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/j.engfracmech.2005.10.013, Vol.73, pp.939-952, 2006Abstract:The paper presents an analysis of cracking and delamination of an elastic plate bonded to a rigid substrate. The plate is subjected to a cyclic temperature loading. The bond between the plate and the substrate is simulated using rigid–frictional and rigid–cohesive–frictional interface models. The states of adaptation or incremental failure are distinguished in the case of the softening interfacial law. The proposed modelling is validated to predict fragmentation of a concrete pavement subjected to temperature loading. The obtained results can serve as reference solutions for numerical calculations of more complex cases.Keywords:Cohesive zone modelling, Segmentation cracking, Delamination, Cyclic loading, Temperature loading 52 Feng Z.-Q., Hjiaj M., de Saxcé G., Mróz Z., Influence of frictional anisotropy on contacting surfaces during loading/unloading cycles, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, ISSN: 0020-7462, DOI: 10.1016/j.ijnonlinmec.2006.08.002, Vol.41, No.8, pp.936-948, 2006Feng Z.-Q., Hjiaj M., de Saxcé G., Mróz Z., Influence of frictional anisotropy on contacting surfaces during loading/unloading cycles, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, ISSN: 0020-7462, DOI: 10.1016/j.ijnonlinmec.2006.08.002, Vol.41, No.8, pp.936-948, 2006Abstract:This paper presents numerical investigations on the loading and unloading of a three-dimensional body in frictional contact with a rigid foundation. The evolution of the sliding process during loading/unloading cycles is analyzed. The important case of anisotropy is examined along with the effect of the sliding rule. The solution algorithm is based on a variational inequality which combine the contact problem and the frictional problem. The numerical results of the punch problem show the hysteretic and irreversible behavior occurring when friction is anisotropic.Keywords:Elliptic friction criterion, non-associated slip rile, Uzawa algorithm, Cyclic loading 53 Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Discrete element method applied to multiobjective optimization of discharge flow parameters in hoppers, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-005-0596-z, Vol.31, pp.163-175, 2006Balevičius R., Kačianauskas R., Mróz Z., Sielamowicz I., Discrete element method applied to multiobjective optimization of discharge flow parameters in hoppers, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-005-0596-z, Vol.31, pp.163-175, 2006Abstract:Multiobjective approach for optimization of the discharge flow parameters of viscoelastic frictional granular material in a wedge-shaped hopper with fixed outlet orifice is considered. The discharge time and the discharge flow rate are taken as optimality criteria, while the discharge mass of material and the shape of the hopper are considered as design variables. The discrete concept and numerical discrete element method (DEM) are applied to the analysis of granular flow. The filling problem considered as numerical generation of the initial conditions for discharge flow was initially solved. The presented DEM model was validated by examining the wall pressures and comparing them with the results of classical macroscopic pressure prediction. Variation of optimality criteria and Pareto set is demonstrated by the numerical results. Sensitivity of optimality criteria to interparticle friction is also investigated.Keywords:Viscoelastic granular material, Hopper, Discrete element method, Optimization of flow parameters 54 Mróz Z., Kowalczyk-Gajewska K., Maciejewski J., Pęcherski R.B., Tensile or compressive plastic deformation of cylinders assisted by cyclic torsion, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.58, No.6, pp.497-527, 2006Mróz Z., Kowalczyk-Gajewska K., Maciejewski J., Pęcherski R.B., Tensile or compressive plastic deformation of cylinders assisted by cyclic torsion, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.58, No.6, pp.497-527, 2006Abstract:Technological metal forming processes of extrusion, forging and rolling with imposed cyclic torsion or shear deformation have been recently studied in view of their advantages with respect to monotonic loading processes, cf. Bochniak and Korbel [2–4]. The present work is aimed to analyze such process in the case of simple tension or compression of a cylindrical tube with imposed cyclic torsional deformation. The material element response is assumed to be rigid-perfectly plastic or elastic-perfectly plastic. For these models, the analytical solutions can be provided for the steady cyclic responses and the effect of two process parameters, namely the ratio of shear and axial strain rates η and the amplitude of shear strain γm , can be clearly demonstrated. Three different regimes of cyclic response can be visualized in the plane η, γm. The cyclic response of a cylinder under combined axial compression and cyclic torsion is predicted by considering a simplified model of a set of concentric tubes and neglecting their radial stress interaction. The axial force and torsional moment are then specified by averaging the responses of consecutive tubes. The cyclic response diagrams for the cylinder are then generated in terms of axial force and torsional moment related to axial deformation and angle of twist Keywords:cyclic torsion, plastic deformation of cylinders, elastic-perfectly plastic model, rigid-perfectly plastic model, analytical solutions of cyclic response of a cylinder 55 Dems K., Mróz Z., Application of thermographic fields in identification of structural properties and defects, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.13, No.1, pp.3-19, 2006Dems K., Mróz Z., Application of thermographic fields in identification of structural properties and defects, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.13, No.1, pp.3-19, 2006Abstract:The detection of defects as well as their location, orientation and size is performed using measurements of surface temperature either at some selected points or on selected surface areas or lines. The response temperature of a structure is caused by statically, quasi-statically or dynamically applied thermal load on some structural boundary parts or within its domain. On the basis of results of measurements, an inverse heat transfer problem is formulated for a model structure and next solved. The inverse solution is constructed by minimizing the properly defined distance norm of measured and model temperatures. The model temperature distribution is calculated using the finite element model of a structure, while in minimizing the distance norm functional the gradient-oriented methods are used. The proper sensitivities of introduced identification functional are also derived. Some simple examples illustrate the applicability of the proposed approach.Keywords:identification, sensitivity, thermographic methods, path-independent integrals 56 Mróz Z., Bojczuk D., Topological sensitivity derivative: application in optimal design and material science, FOUNDATIONS OF CIVIL AND ENVIRONMENTAL ENGINEERING, ISSN: 1642-9303, Vol.7, pp.229-250, 2006Mróz Z., Bojczuk D., Topological sensitivity derivative: application in optimal design and material science, FOUNDATIONS OF CIVIL AND ENVIRONMENTAL ENGINEERING, ISSN: 1642-9303, Vol.7, pp.229-250, 2006Abstract:The concept of topological derivative is introduced and applied to optimal design of structural elements and to study the material microstructure evolution. For structural design the objective function and constraints provide the optimal design, for material microstructure the free energy and dissipation function generate the process of evolution such as phase transformation, crack growth or void generation. Three general modes of topology variation have been considered: generation of new elements, removing of the existing elements and a substitution of the existing elements by new elements. The cases of infinitesimal and finite topology variations have been discussed and illustrated by examples.Keywords:topological derivative, finite topology variation, structure and mate-rial evolution, optimal topology and shape 57 Páczelt I., Mróz Z., On optimal contact shapes generated by wear, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1321, Vol.63, pp.1250-1287, 2005Páczelt I., Mróz Z., On optimal contact shapes generated by wear, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1321, Vol.63, pp.1250-1287, 2005Abstract:The optimal shape design of contacting surfaces has usually been aimed at controlling the contact pressure distribution. However, a much wider class of contact optimization problems can be formulated by maximizing contact force or displacement, torsional moment, or minimizing the friction dissipation. The special classes of optimization problems are considered, namely, minimization of generalized wear volume rate, minimization of generalized friction dissipation power and minimization of the generalized wear dissipation power depending on both normal pressure and slip velocity. The specific wear rule was assumed and the optimality conditions are derived. They generate optimal contact pressure distribution and the corresponding optimal wear rate. The optimization problems are reduced to non-linear programming problems and for their solution a special iteration process is used. The wear process is analysed in two specific cases. First, when the relative sliding velocity between bodies is constant and the second case, when one of bodies rotates with respect to another body. For rotational motion the problem of minimization of friction dissipation power is considered by applying the technique of control of contact pressure distribution and minimization of the generalized friction dissipation power with a new control parameter q. It is demonstrated that the wear dissipation power at the contact surface is minimal in the steady state of wear process and in many cases corresponds to the uniform wear rate. The illustrative examples for rotating bodies demonstrate the evolution of wear process toward a steady state. The minimization of the generalized wear volume rate and of generalized friction dissipation power does not induce the steady state of wear process in the rotation motion. 58 Białas M., Mróz Z., Modelling of progressive interface failure under combined normal compression and shear stress, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/j.ijsolstr.2005.01.006, Vol.42, No.15, pp.4436-4467, 2005Białas M., Mróz Z., Modelling of progressive interface failure under combined normal compression and shear stress, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/j.ijsolstr.2005.01.006, Vol.42, No.15, pp.4436-4467, 2005Abstract:The present work is concerned with an analysis of progressive interface failure under normal compressive stress and varying shear stress using the cohesive crack model. The softening model is assumed and frictional linear stress at contact is accounted for. A monotonic loading in anti-plane shear of an elastic plate bonded to a rigid substrate is considered. An analytical solution is obtained by neglecting the effect of minor shear stress component in the plate. The elastic and plate interface compliances are included into the analysis. Three types of solutions are distinguished in the progressive delamination analysis, namely short, medium and long plate solutions. The analysis of quasi-static progressive delamination process clarifies the character of critical points and post-critical response of the plate. The analytical solution provides a reference benchmark for numerical algorithms of analysis of progressive interface delamination. The case of a rigid–softening interface was treated in a companion paper, where also cyclic loading was considered.Keywords:Interface, Debonding, Cohesive zone, Instability points 59 Mróz Z., Garstecki A., Optimal loading conditions in the design and identification of structures. Part I: Discrete formulation, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-004-0474-0, Vol.29, No.1, pp.1-18, 2005Mróz Z., Garstecki A., Optimal loading conditions in the design and identification of structures. Part I: Discrete formulation, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-004-0474-0, Vol.29, No.1, pp.1-18, 2005Abstract:The paper is concerned with a class of structural optimization problems for which loading distribution and orientation are unspecified. The optimal loading conditions correspond to the extremal structural response, which can be used in assessment of structural safety or in generating the maximum structure stiffness or compliance. In identification problems the optimal load distribution is selected in order to minimize the distance norm between model prediction and experimental data. The sensitivity derivatives and optimality conditions are derived in the paper using discretized formulations. The generalized coaxiality conditions of loading and displacement or adjoint displacement vectors generate eigenvalue problems specifying stationary solutions. The paper is illustrated by examples of optimal loading distribution in structure design and identification. Keywords:optimization, sensitivity analysis, structural identification, variable loading conditions 60 Bojczuk D., Mróz Z., Determination of optimal actuator forces and positions in smart structures using adjoint method, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-005-0517-1, Vol.30, No.4, pp.308-319, 2005Bojczuk D., Mróz Z., Determination of optimal actuator forces and positions in smart structures using adjoint method, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-005-0517-1, Vol.30, No.4, pp.308-319, 2005Abstract:The problem of optimal design of structures with active support is analyzed in the paper. The sensitivity expressions with respect to the generalized force and the position of actuator are derived by the adjoint structure approach. Next, the optimality conditions are formulated by means of an introduced Lagrangian function. The problem of introduction of a new actuator is also considered and the condition of modification is expressed by means of the topological derivative. The obtained sensitivity formula, optimality conditions and modification conditions are applied in the optimization algorithm with respect to the number, positions and generalized forces of the actuators. Numerical examples of optimal control of beams illustrate the procedure proposed in the paper. Keywords:Smart structures, Actuators, Adjoint method, Optimal active support 61 Mróz Z., Seweryn A., Tomczyk A., Fatigue crack growth prediction accounting for the damage zone, FATIGUE AND FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, ISSN: 8756-758X, DOI: 10.1111/j.1460-2695.2004.00829.x, Vol.28, pp.61-71, 2005Mróz Z., Seweryn A., Tomczyk A., Fatigue crack growth prediction accounting for the damage zone, FATIGUE AND FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, ISSN: 8756-758X, DOI: 10.1111/j.1460-2695.2004.00829.x, Vol.28, pp.61-71, 2005Abstract:The present paper is concerned with modelling of fatigue crack initiation and propagation by applying the non-local critical plane model, proposed by Seweryn and Mróz. Using the linear elastic stress field at the front of a crack or sharp notch the damage growth on a physical plane is specified in terms of mean values of stress and strength functions. When the damage zone reaches a critical length, crack growth accompanies damage evolution. The model is applied to study crack propagation under cyclically varying tension compression and the predictions are compared with experimental data. The evolution of the damage zone and crack propagation in the biaxial case is considered next. 62 Mróz Z., Białas M., A simplified analysis of interface failure under compressive normal stress and monotonic or cyclic shear loading, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.417, Vol.29, No.4, pp.337-368, 2005Mróz Z., Białas M., A simplified analysis of interface failure under compressive normal stress and monotonic or cyclic shear loading, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.417, Vol.29, No.4, pp.337-368, 2005Abstract:Interface damage and delamination is usually accompanied by frictional slip at contacting interfaces under compressive normal stress. The present work is concerned with an analysis of progressive interface failure using the cohesive crack model with the critical stress softening and frictional traction present at the contact. Both monotonic and cyclic loadings are considered for anti-plane shear of an elastic plate bonded to a rigid substrate by means of cohesive interface. An analytical solution can be obtained by neglecting the effect of minor shear stress component. The analysis of progressive delamination process revealed three solution types, namely: short, medium and long plate solutions. The long plate solution was obtained under an assumption of quasistatic progressive growth of the delamination zone. In view of snap back response, the quasistatic deformation process cannot be executed by either traction or displacement control. The states of frictional slip accompanied by shake down or incremental failure are distinguished in the case of cyclic loading, related to load amplitude and structural dimensions. The analysis provides a reference solution for numerical treatment of more complex cases. 63 Kačianauskas R., Mróz Z., Żarnovskij V., Stupak E., Three-dimensional correction of the stress intensity factor for plate with a notch, INTERNATIONAL JOURNAL OF FRACTURE, ISSN: 0376-9429, DOI: 10.1007/s10704-005-4401-1, Vol.136, pp.75-98, 2005Kačianauskas R., Mróz Z., Żarnovskij V., Stupak E., Three-dimensional correction of the stress intensity factor for plate with a notch, INTERNATIONAL JOURNAL OF FRACTURE, ISSN: 0376-9429, DOI: 10.1007/s10704-005-4401-1, Vol.136, pp.75-98, 2005Abstract:The 3D effects of the 2D mode I stress intensity factor for the plate with a V-shaped straight through-thickness notch are investigated by the finite element method and three-dimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (out-of-plane degree of freedom). The 3D finite element mesh generator combining the 2D in-plane adaptive unstructured mesh with the structured through-thickness mesh Is developed and applied for the analysis purposes. Three-dimensionality was examined by using two independent indicators, namely, stress- or strain-based constraint factors. The three-point bend and tensile center-cracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for three-point bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile center-cracked plate demonstrated a different nature of the 3D SIF profile, which cannot be simply explained as a transitional state between plain strain and plain stress. Therefore, the suggested 3D correction concept is of a particular character.Keywords:Constraint factor, finite element method, plate with a notch, three-dimensional stress intensity factor 64 Białas M., Majerus P., Herzog R., Mróz Z., Numerical simulation of segmentation cracking in thermal barrier coatings by means of cohesive zone elements, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 0921-5093, DOI: 10.1016/j.msea.2005.08.208, Vol.412, pp.241-251, 2005Białas M., Majerus P., Herzog R., Mróz Z., Numerical simulation of segmentation cracking in thermal barrier coatings by means of cohesive zone elements, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 0921-5093, DOI: 10.1016/j.msea.2005.08.208, Vol.412, pp.241-251, 2005Abstract:The paper presents comparative experimental and numerical studies of segmentation cracking of thermal barrier coatings (TBCs) during three point bending tests. The finite element simulation of failure development was performed using a cohesive zone approach. Acoustic emission (AE) technique and in situ observations by a charge-coupled device (CCD) camera allowed to determine critical strain values correlated with the damage evolution. Location of crack initiation and crack propagation paths up to macroscopic failure were investigated for as-received and annealed specimens. The results of the numerical simulations and of the experiment were quantitatively similar. The influence of critical energy release rate on crack patterns was examined, resulting in the increase of crack numbers due to decreased value of GIGI. This explains the good spallation resistance of electron beam-physical vapour deposition (EB-PVD) coatings, where GIGI is lower than in the case of air plasma sprayed (APS) thermal barrier coatings. Lower value of GIGI stimulates segmentation cracking and reduces delamination, as observed within electron beam-physical vapour deposition coatings.Keywords:Cohesive zone modelling, Segmentation cracking, Thin film coating, Bending test 65 Ivanova J., Valeva V., Mróz Z., Interphase model for a multilayer structures applied in heat conduction problems, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.34, pp.15-30, 2005 66 Hjiaj M., Feng Z.-Q., de Saxcé G., Mróz Z., Three-dimensional finite element computations for frictional contact problems with non-associated sliding rule, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1037, Vol.60, No.12, pp.2045-2076, 2004Hjiaj M., Feng Z.-Q., de Saxcé G., Mróz Z., Three-dimensional finite element computations for frictional contact problems with non-associated sliding rule, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1037, Vol.60, No.12, pp.2045-2076, 2004Abstract:This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non-associated.The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non-associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi-axes ratio. The frictional contact law and its inverse are derived from a single non-differentiable scalar-valued function, called a bi-potential. The convexity properties of the bi-potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time-integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor–corrector step addresses all cases (sticking, sliding, no-contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour. 67 Kucharski S., Mróz Z., Identification of material parameters by means of compliance moduli in spherical indentation test, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 0921-5093, DOI: 10.1016/j.msea.2004.03.030, Vol.379, No.1-2, pp.448-456, 2004Kucharski S., Mróz Z., Identification of material parameters by means of compliance moduli in spherical indentation test, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 0921-5093, DOI: 10.1016/j.msea.2004.03.030, Vol.379, No.1-2, pp.448-456, 2004Abstract:An identification method of elastic and plastic hardening parameters is proposed by measuring compliance moduli in loading and unloading in the spherical indentation test. The loading program is composed of consecutive loading and unloading steps from which the compliance moduli are determined from the load–penetration (P–h) curve. The hardening parameters k and m occurring in the plastic hardening curve Full-size image (<1 K) are then specified. Identification of materials described by a more complex three parameters constitutive law εp=((σ−σy)/k)′1/m′, where σy denotes the yield stress, is also analysed. The identification of Young’s modulus from the indentation test is also presented.Keywords:Spherical indentation test, Identification, Elasto-plastic material properties, Indentation compliance moduli 68 Seweryn A., Tomczyk A., Mróz Z., A non-local fatigue crack growth model and its experimental verification, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.42, No.1, pp.69-82, 2004Seweryn A., Tomczyk A., Mróz Z., A non-local fatigue crack growth model and its experimental verification, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.42, No.1, pp.69-82, 2004Abstract:The present paper is concerned with the modelling of fatigue crack initiation and propagation by applying the non-local critical plane model, proposed by Seweryn and Mróz (1996, 1998). Using the linear elastic stress field at the front of a crack or sharp notch, the damage growth on a physical plane is specified in terms of mean values of the stress and strength function. The model is applied to study crack propagation under cyclically varying tension-compression conditions. The predictions are compared with experimental data.Keywords:fatigue, damage accumulation, crack propagation 69 Boukpeti N., Mróz Z., Drescher A., Modeling rate effects in undrained loading of sands, Canadian Geotechnical Journal, ISSN: 0008-3674, DOI: 10.1139/t03-077, Vol.41, No.2, pp.342-350, 2004Boukpeti N., Mróz Z., Drescher A., Modeling rate effects in undrained loading of sands, Canadian Geotechnical Journal, ISSN: 0008-3674, DOI: 10.1139/t03-077, Vol.41, No.2, pp.342-350, 2004Abstract:The present technical note extends the previous work by the authors concerned with formulation of a constitutive model of elastoplastic response of sands (Superior sand model) and its application to the analyses of static liquefaction and instability states in triaxial compression and extension occurring in the undrained deformation of saturated granular materials. To account for time-dependent behavior and strain rate effects, an elastic, viscoplastic extension of the model to triaxial compression is proposed. The constitutive equations derived are used to predict the model response in different loading histories. In particular, strain rate and stress rate effects and undrained creep deformation for specified stress components are discussed in detail. Comparison of model predictions with available experimental data also is provided.Key words: saturated sand, constitutive model, elasticviscoplastic behavior. 70 Hjiaj M., Feng Z.-Q., de Saxcé G., Mróz Z., On the modelling of complex anisotropic frictional contact laws, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/j.ijengsci.2003.10.004, Vol.42, No.10, pp.1013-1034, 2004Hjiaj M., Feng Z.-Q., de Saxcé G., Mróz Z., On the modelling of complex anisotropic frictional contact laws, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/j.ijengsci.2003.10.004, Vol.42, No.10, pp.1013-1034, 2004Abstract:In this paper, the formulation of complex anisotropic frictional models with orthotropic friction condition and non-associated sliding rule is discussed. The friction law is described by a superellipse, which allow to consider a wide range of convex friction condition by simply varying the roundness factor affecting the shape of the limit surface. The sliding potential is also a superellipse but with a different semi-axis ratio, which lead to a non-associated sliding rule. For bodies in contact, the Signorini conditions can be formulated in terms of velocities and combined with the sliding rule to give the frictional contact law describing interfacial interactions. Its is shown that the frictional contact law as well as its inverse can be derived from the same scalar valued function called bi-potential. Due to the non-associated nature of the law, this relation is implicit. The advantage of the present formulation lies in the existence of stationary points of a functional, called bi-functional, that depends on both the displacements and the stresses.Keywords:Superelliptic friction criterion, Non-associated sliding rule, Bi-potential, Variational formulation 71 Mróz Z., Bojczuk D., Finite topology variations in optimal design of structures, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-003-0289-4, Vol.25, No.3, pp.153-173, 2003Mróz Z., Bojczuk D., Finite topology variations in optimal design of structures, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/s00158-003-0289-4, Vol.25, No.3, pp.153-173, 2003Abstract:The method of optimal design of structures by finite topology modification is presented in the paper. This approach is similar to growth models of biological structures, but in the present case, topology modification is described by the finite variation of a topological parameter. The conditions for introducing topology modification and the method for determining finite values of topological parameters characterizing the modified structure are specified. The present approach is applied to the optimal design of truss, beam, and frame structures. For trusses, the heuristic algorithm of bar exchange is proposed for minimizing the global compliance subject to a material volume constraint and it is extended to volume minimization with stress and buckling constraints. The optimal design problem for beam and frame structures with elastic or rigid supports, aimed at minimizing the structure cost for a specified global compliance, is also considered.Keywords:optimal topology, finite topology modifications, structure evolution, truss and frame structures 72 Kowalczyk K., Mróz Z., Description of anisotropy of textured metals using macro and micro models, JOURNAL DE PHYSIQUE IV, ISSN: 1155-4339, DOI: 10.1051/jp4:20030188, Vol.105, pp.199-206, 2003Kowalczyk K., Mróz Z., Description of anisotropy of textured metals using macro and micro models, JOURNAL DE PHYSIQUE IV, ISSN: 1155-4339, DOI: 10.1051/jp4:20030188, Vol.105, pp.199-206, 2003Abstract:In the paper description of anisotropy of textured metals using macro and micro models is compared. In the present macro-approach the texture anisotropy is described by introducing a second order microstructure tensor whose principal directions specify the orthotropy axes. A scalar orientation parameter $\eta$ is introduced in order to specify the relative orientation of the generalized traction vector with respect to anisotropy axes. The yield stress is assumed to depend on the parameter $\eta$ with specific forms introduced in order to provide quantitative description of yield stress variation with loading orientation. The phenomenological approach is next confronted with the microstructural approach based on the analysis of crystallographic slip and induced lattice reorientation in a representative grain aggregate. The resulting yield surface for polycrystalline aggregate is then compared with the macroscopic description based on the orientational variation of the yield stress. The proposed macro description seems much simpler from micro-approach and could prove convenient in the analysis of technological processes for textured materials. 73 Mróz Z., Sielamowicz I., Deformation Zones in Granular Materials in Hoppers During Filling and Emptying Processes, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867-888X, Vol.51, No.4, pp.461-491, 2003Mróz Z., Sielamowicz I., Deformation Zones in Granular Materials in Hoppers During Filling and Emptying Processes, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867-888X, Vol.51, No.4, pp.461-491, 2003Abstract:The present paper is concerned with the simplified analysis of deformation and stress states in converging hoppers during filling and discharge of a granular material. The equilibrium conditions and stress-strain relations are satisfied for cylindrical slice elements assuming dependence of displacement and stress on radial coordinate. The elastic or elasto-plastic material model is used with the Coulomb yield condition and non-associated flow rule. The paper presents a detailed analysis of pressure evolution of a granular material on a hopper wall during the emptying process when the initial active state of pressure is transformed into the passive state. The growth of wall pressure associated with this process is demonstrated. The analytical treatment presented in this paper can be compared with the respective finite element solution. 74 Stupkiewicz S., Mróz Z., Phenomenological model of real contact area evolution with account for bulk plastic deformation in metal forming, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/S0749-6419(01)00037-7, Vol.19, No.3, pp.323-344, 2003Stupkiewicz S., Mróz Z., Phenomenological model of real contact area evolution with account for bulk plastic deformation in metal forming, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/S0749-6419(01)00037-7, Vol.19, No.3, pp.323-344, 2003Abstract:A phenomenological description of the evolution of real contact area in metal forming processes is presented with account for the effect of bulk plastic flow. A thin surface layer is considered and assumed to be weakened by the localized plastic deformation around surface asperities. The yield condition of this layer is expressed in terms of contact stresses, plastic strain rate of the bulk and real contact area fraction and its rate. The model applicability is illustrated by comparing its predictions of real contact area variation, depending on bulk strain, with predictions of micro-mechanical models and with experimental data.Keywords:Cutting and forming, Constitutive behaviour, Ideally plastic material, Frictional contact 75 Białas M., Mróz Z. , Drescher A., Constitutive model for static liquefaction, International Journal of Geomechanics, ISSN: 1532-3641, DOI: 10.1061/(ASCE)1532-3641(2003)3:2(133)#sthash.LLxWvMhd.dpuf, Vol.3, No.2, pp.133-144, 2003Białas M., Mróz Z. , Drescher A., Constitutive model for static liquefaction, International Journal of Geomechanics, ISSN: 1532-3641, DOI: 10.1061/(ASCE)1532-3641(2003)3:2(133)#sthash.LLxWvMhd.dpuf, Vol.3, No.2, pp.133-144, 2003Abstract:A general, three-dimensional formulation of the elastoplastic refined Superior sand constitutive model is presented. The model is aimed at realistic simulation of liquefaction phenomena occurring in loose saturated granular materials under monotonic static loading. The isotropic hardening/softening is related to plastic deformation and distance to a reference yield surface. The nonassociated flow rule is used with the closed yield surface introduced previously in the Superior sand model. The refined model accounts for the different response of materials with different deposition densities. The model prediction of drained and undrained plane-strain compression is presented and compared with the response in triaxial compression/extension loading. Static and kinematic instability states also are discussed. 76 Hjiaj M., de Saxcé G., Mróz Z., A variational inequality-based formulation of the frictional contact law with a non-associated sliding rule, EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, ISSN: 0997-7538, DOI: 10.1016/S0997-7538(01)01183-4, Vol.21, No.1, pp.49-59, 2002Hjiaj M., de Saxcé G., Mróz Z., A variational inequality-based formulation of the frictional contact law with a non-associated sliding rule, EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, ISSN: 0997-7538, DOI: 10.1016/S0997-7538(01)01183-4, Vol.21, No.1, pp.49-59, 2002Abstract:We present a variational formulation of a complex frictional contact law with anisotropic friction condition and a non-associated sliding rule. The distinguishing characteristic of the proposed formulation is that the interface law, as well as its inverse, derive from a single scalar-valued function called bi-potential. This function, which depends on both the velocities and the associated forces, is split into the sum of two dual pseudo-potentials for standard multivalued laws. The main advantages of the formalism are the compact form taken by the present complex law and convexity property of the bi-potential that can be exploited for numerical purposes. 77 Mróz Z., Maciejewski J., Failure criteria of anisotropically damaged materials based on the critical plane concept, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.207, Vol.26, No.4, pp.407-431, 2002Mróz Z., Maciejewski J., Failure criteria of anisotropically damaged materials based on the critical plane concept, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.207, Vol.26, No.4, pp.407-431, 2002Abstract:The damage state of a cracked material is assumed to be specified by crack density distribution on physical planes. The critical plane approach is used with account for damaged and intact area fractions on the plane. The maximum of failure function is specified for all potential failure planes and the critical plane orientation is determined. The resulting failure condition is applied to study strength evolution for triaxially compressed specimens with varying orientation of principal stress and damage tensor axes. Both Coulomb and non-linear failure conditions of Mohr type are applied to specify the representative critical plane. A general stress state is considered and the failure condition is specified for different relative orientations of orthotropy and principal stress axes. 78 Mróz Z., Oliferuk W., Energy balance and identification of hardening moduli in plastic deformation processes, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/S0749-6419(00)00103-0, Vol.18, No.3, pp.379-397, 2002Mróz Z., Oliferuk W., Energy balance and identification of hardening moduli in plastic deformation processes, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/S0749-6419(00)00103-0, Vol.18, No.3, pp.379-397, 2002Abstract:The hardening moduli Hr and Hd of plastic deformation associated with the free energy and dissipation function in a representative material element are defined analytically and specified experimentally for three materials. Besides the stress–strain curve and work expended during the deformation process, variation of the hardening moduli with plastic deformation is also determined for austenitic steel, austenitic-ferritic steel and Fe–Si alloy.Keywords:Thermomechanical processes, Hardening modulus, Polycrystalline material, Energy methods, Mechanical testing 79 Boukpeti N., Mróz Z., Drescher A., A model for static liquefaction in triaxial compression and extension, OPTIMAL CONTROL APPLICATIONS & METHODS, ISSN: 0143-2087, DOI: 10.1139/t02-066, Vol.39, No.6, pp.1243-1253, 2002Boukpeti N., Mróz Z., Drescher A., A model for static liquefaction in triaxial compression and extension, OPTIMAL CONTROL APPLICATIONS & METHODS, ISSN: 0143-2087, DOI: 10.1139/t02-066, Vol.39, No.6, pp.1243-1253, 2002Abstract:The response of the elastoplastic refined Superior sand constitutive model in undrained triaxial compression and extension tests is presented. The model is aimed at realistic simulation of liquefaction occurring in loose, saturated, granular materials under monotonic static loading. The yield surface introduced previously in the original Superior sand model is modified, and a non-associated flow rule is used. The isotropic hardeningsoftening is related to plastic deformation and distance to a reference yield curve. The refined model accounts for the different response of materials with different deposition densities. The model prediction of undrained triaxial compression and extension tests is compared with experimental results. The higher tendency for liquefaction response in extension is well described. Instability and phase-transformation states also are discussed, and the energy of liquefaction is quantified.Key words: static liquefaction, constitutive model, triaxial tests, liquefaction energy. 80 Valeva V., Ivanova J., Mróz Z., Parametric analysis of the decay rate of end effects in heat conduction for multi-layered semi-infinite sandwich structures, Journal of Theoretical and Applied Mechanics, BULGARIAN ACADEMY OF SCIENCES, ISSN: 1313-9665, Vol.32, No.4, pp.39-52, 2002Valeva V., Ivanova J., Mróz Z., Parametric analysis of the decay rate of end effects in heat conduction for multi-layered semi-infinite sandwich structures, Journal of Theoretical and Applied Mechanics, BULGARIAN ACADEMY OF SCIENCES, ISSN: 1313-9665, Vol.32, No.4, pp.39-52, 2002Abstract:This article is concerned with the effect of imperfect interfaces on the decay of end effect for heat conduction in non-symmetric sandwich strip with - layers. The constituent layers are isotropic and the interface conditions between the layers are assumed to be either LC-type or HC-type at vanishing temperature at the bottom and top side of the strip. The characteristic decay length in all considered cases for three-layered sandwich strip is numerically calculated and represented by the smallest real and positive root of a corresponding transcendental equation. The results of parametric analysis of decay rate depending on volume fraction and heat conductivity of constituents provided for three-layered sandwich strip are illustrated in figures and discussed. Some optimal parameters for the considered structure at which the maximal value of the decay rate is reached are proposed.Keywords:decay rate of end effects, heat condition, semi-infinite sandwich structure 81 Pietruszczak S., Mróz Z., On failure criteria for anisotropic cohesive-frictional materials, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.141, Vol.25, No.5, pp.509-524, 2001Pietruszczak S., Mróz Z., On failure criteria for anisotropic cohesive-frictional materials, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.141, Vol.25, No.5, pp.509-524, 2001Abstract:Anisotropic failure criteria are formulated using two different approaches. The first one employs a spatial distribution of strength parameters and defines the failure condition in terms of traction components acting on the critical plane. The second one incorporates a microstructure tensor and the relevant mixed invariants. Both formulations are illustrated by some numerical examples. In particular, the variation of strength with orientation of the sample is examined for a series of uniaxial compression tests. 82 Leśniewska D., Mróz Z., Study of evolution of shear band systems in sand retained by flexible wall, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.160, Vol.25, No.9, pp.909-932, 2001Leśniewska D., Mróz Z., Study of evolution of shear band systems in sand retained by flexible wall, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.160, Vol.25, No.9, pp.909-932, 2001Abstract:The present paper is concerned with the study of the evolution of regular patterns of shear bands observed experimentally (cf. Milligan, 1974), and provides an extension of the previous work published by the same authors. The purpose of this paper is to present an improved version of a simple theoretical model, derived basically from a classical equilibrium of the Coulomb wedge. This model constitutes a modified version of an extension of the classical Coulomb wedge analysis by assuming that soil parameters are varying during the deformation process and the initial configuration at which limit equilibrium occurs evolves toward a new equilibrium configuration. The application of the model in the analysis of shear band pattern observed in dredged model tests on cantilever walls provided realistic simulation of consecutive shear band formation. 83 Kucharski S., Mróz Z., Identification of plastic hardening parameters of metals from spherical indentation tests, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 0921-5093, DOI: 10.1016/S0921-5093(01)01334-X, Vol.318, No.1-2, pp.65-76, 2001Kucharski S., Mróz Z., Identification of plastic hardening parameters of metals from spherical indentation tests, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 0921-5093, DOI: 10.1016/S0921-5093(01)01334-X, Vol.318, No.1-2, pp.65-76, 2001Abstract:Using the two-parameter power hardening rule σ=kεpm, the parameters k and m are identified from spherical indentation loading–unloading tests which account for the variation of the indentation profile during elastic unloading and sphere deformation. The predicted and measured stress–strain curves are compared for several materials. Both experimental and actual data for 18G2A low-alloy steel are used to assess the accuracy of the identification procedure. Finally, identification of the stress–strain curve of an aluminium alloy is demonstrated.Keywords:Spherical indentation tests, Plastic, Low-alloy steel, Metals 84 Giambanco G., Mróz Z., The Interphase Model for the Analysis of Joints in Rock Masses and Masonry Structures, MECCANICA, ISSN: 0025-6455, DOI: 10.1023/A:1011957217840, Vol.36, No.1, pp.111-130, 2001Giambanco G., Mróz Z., The Interphase Model for the Analysis of Joints in Rock Masses and Masonry Structures, MECCANICA, ISSN: 0025-6455, DOI: 10.1023/A:1011957217840, Vol.36, No.1, pp.111-130, 2001Abstract:To study the response of cementitious joints in rock masses or masonry structures, the model of interphase is considered for which the contact stresses and strains interact with the internal stresses or strains within the joint. The frictional slip and sliding effects are then combined with the inelastic deformations of the joint. The constitutive model of the joint is analysed by assuming two interfaces separating the joint from the adjacent material. The case of a cementitious layer interposed between two rigid bodies is treated in detail.Keywords:Softening, Contact, Interfaces, Cohesive joint 85 Stupkiewicz S., Mróz Z., Modelling of friction and dilatancy effects at brittle interfaces for monotonic and cyclic loading, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.39, No.3, pp.707-739, 2001Stupkiewicz S., Mróz Z., Modelling of friction and dilatancy effects at brittle interfaces for monotonic and cyclic loading, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.39, No.3, pp.707-739, 2001Abstract:The most important effects related to monotonic and cyclic response of contact interfaces of brittle materials are analyzed in the paper. Next, the available constitutive models are reviewed with respect to their ability to describe these effects. Several micro-mechanical mechanisms are analyzed including decohesion, interaction of primary and secondary asperities, asperity wear and damage and formation of a third body granular layer. Finally, we propose new formulations of constitutive models for cyclic interface response. 86 Xin-pu S., Mróz Z., Bing-ye X., Constitutive theory of plasticity coupled with orthotropic damage for geomaterials, APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, ISSN: 0253-4827, DOI: 10.1007/BF02438321, Vol.22, No.9, pp.1028-1034, 2001Xin-pu S., Mróz Z., Bing-ye X., Constitutive theory of plasticity coupled with orthotropic damage for geomaterials, APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, ISSN: 0253-4827, DOI: 10.1007/BF02438321, Vol.22, No.9, pp.1028-1034, 2001Abstract:Constitutive theory of plasticity coupled with orthotropic damage for geomaterials was established in the framework of irreversible thermodynamics. Prime results include: 1) evolution laws are presented for coupled evolution of plasticity and orthotropic damage; 2) the orthotropic damage tensor is introduced into the Mohr-Coulomb criterion through homogenization. Both the degradation of shear strength and degradation of friction angle caused by damage are included in this model. The dilatancy is calculated with the so-called damage strain.Keywords:damage plasticity, coupling, dilatancy, geomaterial 87 Sergeyev O., Mróz Z., Sensitivity analysis and optimal design of 3D frame structures for stress and frequency constraints, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/S0045-7949(99)00088-7, Vol.75, No.2, pp.167-185, 2000Sergeyev O., Mróz Z., Sensitivity analysis and optimal design of 3D frame structures for stress and frequency constraints, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/S0045-7949(99)00088-7, Vol.75, No.2, pp.167-185, 2000Abstract:The present paper deals with the problem of determining the optimal joint positions and cross-sectional parameters of linearly elastic space frames with imposed stress and free frequency constraints. The frame is assumed to be acted on by different load systems, including temperature and self-weight loads. The stress state analysis includes tension, bending, shear, and torsion of beam elements. By a sequence of quadratic programming problems, the optimal design is attained. The sensitivity analysis of distinct as well as multiple frequencies is performed through analytic differentiation with respect to design parameters. Illustrative examples of optimal design of simple and medium complexity frames are presented, and the particular case of bimodal optimal solution is considered in detail. 88 Pietruszczak S., Mróz Z., Formulation of anisotropic failure criteria incorporating a microstructure tensor, COMPUTERS AND GEOTECHNICS, ISSN: 0266-352X, DOI: 10.1016/S0266-352X(99)00034-8, Vol.26, No.2, pp.105-112, 2000Pietruszczak S., Mróz Z., Formulation of anisotropic failure criteria incorporating a microstructure tensor, COMPUTERS AND GEOTECHNICS, ISSN: 0266-352X, DOI: 10.1016/S0266-352X(99)00034-8, Vol.26, No.2, pp.105-112, 2000Abstract:Anisotropy is inherently related to microstructural arrangement within a representative volume of material. The microstructure can be represented by a second order tensor whose eigenvectors specify the orientation of the axes of material symmetry. In this paper, failure criteria for geomaterials are formulated in terms of the stress state and a microstructure tensor. The classical criteria for isotropic materials are generalized for the case of orthotropy as well as transverse isotropy. The proposed approach is illustrated by a simple example demonstrating the sensitivity of the uniaxial strength of the material to the orientation of the sample relative to the loading direction. 89 Pietruszczak S., Mróz Z., Lewandowski M., Nowicki A., Formulation of anisotropic failure criteria incorporating a microstructure tensor, COMPUTERS AND GEOTECHNICS, ISSN: 0266-352X, DOI: 10.1016/S0266-352X(99)00034-8, Vol.26, No.2, pp.105-112, 2000Pietruszczak S., Mróz Z., Lewandowski M., Nowicki A., Formulation of anisotropic failure criteria incorporating a microstructure tensor, COMPUTERS AND GEOTECHNICS, ISSN: 0266-352X, DOI: 10.1016/S0266-352X(99)00034-8, Vol.26, No.2, pp.105-112, 2000Abstract:Anisotropy is inherently related to microstructural arrangement within a representative volume of material. The microstructure can be represented by a second order tensor whose eigenvectors specify the orientation of the axes of material symmetry. In this paper, failure criteria for geomaterials are formulated in terms of the stress state and a microstructure tensor. The classical criteria for isotropic materials are generalized for the case of orthotropy as well as transverse isotropy. The proposed approach is illustrated by a simple example demonstrating the sensitivity of the uniaxial strength of the material to the orientation of the sample relative to the loading direction. 90 Mróz Z., On the stability of friction contact, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.38, No.2, pp.315-329, 2000Mróz Z., On the stability of friction contact, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.38, No.2, pp.315-329, 2000Abstract:The stability condition (1.2) for frictional contact expressed in terms of potential energy and the dissipation function is applied to analysis of the stability of rigid-sliding and elastic-sliding contacts obeying the Coulomb friction condition and the non-associated sliding rule. Both static and dynamic modes are considered.Keywords:contact friction, stability, static and dynamic modes 91 Xin-pu S., Mróz Z., Shear beam model for interface failure under antiplane shear (I)-Fundamental behavior, APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, ISSN: 0253-4827, DOI: 10.1007/BF02459242, Vol.21, No.11, pp.1221-1228, 2000Xin-pu S., Mróz Z., Shear beam model for interface failure under antiplane shear (I)-Fundamental behavior, APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, ISSN: 0253-4827, DOI: 10.1007/BF02459242, Vol.21, No.11, pp.1221-1228, 2000Abstract:The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elastoplasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concent of ‘cohesive crack’ was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.Keywords:interface layer, cohesive layer, anti-plane shear, shear beam model, failure, instability, damage 92 Xin-pu S., Mróz Z., Shear beam model for interface failure under antiplane shear (II)— Instability, APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, ISSN: 0253-4827, DOI: 10.1007/BF02459243, Vol.21, No.11, pp.1229-1236, 2000Xin-pu S., Mróz Z., Shear beam model for interface failure under antiplane shear (II)— Instability, APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, ISSN: 0253-4827, DOI: 10.1007/BF02459243, Vol.21, No.11, pp.1229-1236, 2000Abstract:Based on the (I) of the present work, the behavior of shear beam model at crack initiation stage andat instable propagation stage was studied. The prime results include:1) discriminant equation which clarifies the mode of instability, snap-back or snap-through, was established;2) analytical solution was given out for the double shear beam and the load-displacement diagram for monotonic loading was presented for a full process; and3) the problem of the energy release induced by instability was discussed.Keywords:interface layer, antiplane shear, failure, shear beam model, instability, snapthrough, snap-back, damage 93 Stupkiewicz S., Mróz Z., A model of third body abrasive friction and wear in hot metal forming, WEAR, ISSN: 0043-1648, DOI: 10.1016/S0043-1648(99)00124-6, Vol.231, No.1, pp.124-138, 1999Stupkiewicz S., Mróz Z., A model of third body abrasive friction and wear in hot metal forming, WEAR, ISSN: 0043-1648, DOI: 10.1016/S0043-1648(99)00124-6, Vol.231, No.1, pp.124-138, 1999Abstract:A model of friction accounting for third body particles at the contact interface is derived from a simple micro-mechanical model of a particle interacting with a hard tool surface and a soft workpiece surface. Also a wear law coupled with this friction model is proposed. When wear of the tool surface is considered, the abrasive contribution of hard particles is only accounted for. The rate of wear is associated with frictional dissipation rate rather than with the product of normal pressure and slip velocity as in the classical Archard wear law. Numerical examples illustrate applicability and properties of the proposed friction and wear model.Keywords:Contact friction, Wear, Hot metal forming, Third body abrasion 94 Nawrocki P., Mróz Z., A constitutive model for rock accounting for viscosity and yield stress degradation, COMPUTERS AND GEOTECHNICS, ISSN: 0266-352X, DOI: 10.1016/S0266-352X(99)00020-8, Vol.25, No.4, pp.247-280, 1999Nawrocki P., Mróz Z., A constitutive model for rock accounting for viscosity and yield stress degradation, COMPUTERS AND GEOTECHNICS, ISSN: 0266-352X, DOI: 10.1016/S0266-352X(99)00020-8, Vol.25, No.4, pp.247-280, 1999Abstract:A viscoplastic constitutive model of rock is proposed for which both yield stress and viscosity undergo variation during the deformation process. The model is initially formulated for a uniaxial stress state; its extension for a general stress state is also provided. Model parameters are determined from compression tests at different values of strain rate, and its application to simulate results of such tests is given. The examples of stress redistribution in a coal seam due to progressing longwall exploitation are presented by applying the developed degradation model. The model provides good simulation of material response in both stable and post-critical stages. 95 Bojczuk D., Mróz Z., Optimal topology and configuration design of trusses with stress and buckling constraints, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01197710, Vol.17, No.1, pp.25-35, 1999Bojczuk D., Mróz Z., Optimal topology and configuration design of trusses with stress and buckling constraints, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01197710, Vol.17, No.1, pp.25-35, 1999Abstract:A heuristic algorithm for optimal design of trusses is presented with account for stress and buckling constraints. The design variables are constituted by cross-sectional areas, configuration of nodes and the number of nodes and bars. Similarly to biological growth models, it is postulated that the structure evolves with the characteristic size parameter and the “bifurcation” of topology occurs with the generation of new nodes and bars in order to minimize the cost function. The first-order sensitivity derivatives provide the necessary information on topology variation and the optimality conditions for configuration and cross-sectional parameters. 96 Mróz Z., Piekarski J., Sensitivity analysis and optimal design of non-linear structures, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/(SICI)1097-0207(19980815)42:7<1231::AID-NME407>3.0.C, Vol.42, No.7, pp.1231-1262, 1998Mróz Z., Piekarski J., Sensitivity analysis and optimal design of non-linear structures, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/(SICI)1097-0207(19980815)42:7<1231::AID-NME407>3.0.C, Vol.42, No.7, pp.1231-1262, 1998Abstract:Sensitivity analysis for non-linear elastic structures in regular and critical states is first discussed including design parameters and initial imperfections. Next, the optimal design problem is formulated by considering imperfect structures and setting constraints on deflections and stresses. For structures with unstable post-critical response the limit load constraint is introduced in the optimization procedure. Several examples of truss optimization are provided. The level of initial imperfections can be regarded as design parameter and specified from the optimal solution. 97 Mróz Z., Stupkiewicz S., Constitutive model of adhesive and ploughing friction in metal-forming processes, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/S0020-7403(97)00055-6, Vol.40, No.2-3, pp.281-303, 1998Mróz Z., Stupkiewicz S., Constitutive model of adhesive and ploughing friction in metal-forming processes, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/S0020-7403(97)00055-6, Vol.40, No.2-3, pp.281-303, 1998Abstract:In metal-forming processes the tool-workpiece interaction is associated with friction forces due to cohesive bonds and ploughing of hard particles or asperities through the interface layer and also with irreversible asperity flattening. In the present work, the combined effect of adhesive and ploughing friction is accounted for by assuming two different length scales of interacting asperities of workpiece and tool. The constitutive model of friction slip is formulated by introducing the representative contact state variables and providing their evolution rules together with friction condition and the non-associated slip rule. The model parameters can be identified from micro-mechanical solutions of asperity flattening and ploughing problems. Also a purely phenomenological model is proposed. The dual asperity model is next applied to predict contact slip and friction response and in numerical analysis of two boundary value problems.Keywords:contact friction, metal forming, asperity flattening, ploughing 98 Seweryn A., Mróz Z., On the criterion of damage evolution for variable multiaxial stress states, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/S0020-7683(97)00121-2, Vol.35, No.14, pp.1589-1616, 1998Seweryn A., Mróz Z., On the criterion of damage evolution for variable multiaxial stress states, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/S0020-7683(97)00121-2, Vol.35, No.14, pp.1589-1616, 1998Abstract:The damage accumulation condition expressed in terms of traction components on a physical plane is discussed for both monotonic and cyclic loading conditions. The crack initiation is assumed to correspond to a critical value of damage reached on the physical plane. For singular stress distribution in the front of sharp notch or crack the non-local condition is formulated. The proposed condition is applied to predict damage distribution within the representative element for cyclic loading conditions. The rosette diagrams are constructed for visualization of damage distribution. The prediction of crack initiation for multiaxial fatigue loading is provided. The second- and fourth-order damage tensors in order to describe damage distribution within the element, and the associated compliance variation are introduced. 99 Nawrocki P., Mróz Z., A viscoplastic degradation model for rocks, INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES, ISSN: 1365-1609, DOI: 10.1016/S0148-9062(98)00012-6, Vol.35, No.7, pp.991-1000, 1998Nawrocki P., Mróz Z., A viscoplastic degradation model for rocks, INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES, ISSN: 1365-1609, DOI: 10.1016/S0148-9062(98)00012-6, Vol.35, No.7, pp.991-1000, 1998Abstract:In this paper a viscoplastic constitutive model for rocks is proposed in which both yield stress and viscosity undergo variation during the deformation process. The model is initially formulated for a uniaxial stress state; its extension to a general stress state has been also presented. Our model is capable to sufficiently well predict both the pre-peak hardening and post-peak softening response of rock material in compression providing good simulation of material response in both stable and post-critical stages of deformation. Such behaviour can be obtained for both low and high strain rates. In our examples, model parameters are determined from uniaxial compression tests performed on sandstone at different strain rates. 100 Dems K., Mróz Z., Sensitivity analysis and optimal design of external boundaries and interfaces for heat conduction systems, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, Vol.21, No.3-4, pp.461-488, 1998Dems K., Mróz Z., Sensitivity analysis and optimal design of external boundaries and interfaces for heat conduction systems, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, Vol.21, No.3-4, pp.461-488, 1998Abstract:A heat conduction problem within a thermal anisotropic solid body is formulated. With respect to an arbitrary thermal functional defined over space domain, its first-order sensitivities with respect to variation of structural material parameters as well as external boundary and internal interfaces are derived using the direct and adjoint approaches. Next, the application of derived sensitivity expressions in optimizing thermal systems is presented and illustrated by some examples. 101 Bojczuk D., Mróz Z., Optimal Design of Trusses with Account for Topology Variation, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905459808945418, Vol.26, No.1, pp.21-40, 1998Bojczuk D., Mróz Z., Optimal Design of Trusses with Account for Topology Variation, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905459808945418, Vol.26, No.1, pp.21-40, 1998Abstract:In this paper, a heuristic algorithm is presented for optimal design of trusses with varying cross-sectional parameters, configuration of nodes, and number of nodes and bars. The algorithm provides new nodes and bars at some states and for the optimal truss configuration. It is assumed that the structure evolves with the overall size parameter and a “bifurcation” of topology occurs with the generation of new nodes, in order to minimize the cost function. Both displacement and stress constraints can be introduced in the optimization procedure. 102 Seweryn A., Poskrobko S., Mróz Z., Brittle Fracture in Plane Elements with Sharp Notches under Mixed-Mode Loading, JOURNAL OF ENGINEERING MECHANICS-ASCE, ISSN: 0733-9399, DOI: 10.1061/(ASCE)0733-9399(1997)123:6(535), Vol.123, No.6, pp.535-543, 1997Seweryn A., Poskrobko S., Mróz Z., Brittle Fracture in Plane Elements with Sharp Notches under Mixed-Mode Loading, JOURNAL OF ENGINEERING MECHANICS-ASCE, ISSN: 0733-9399, DOI: 10.1061/(ASCE)0733-9399(1997)123:6(535), Vol.123, No.6, pp.535-543, 1997Abstract:Plane structural elements with sharp wedge-shaped notches are considered and the conditions for crack initiation are discussed. The use of the Griffith energy condition would require the assumption of pre-existence of a plane crack emanating from the notch vertex at specified direction. To avoid this assumption, a nonlocal crack initiation and propagation condition proposed by Seweryn and Mróz is applied to study crack initiation. This condition is expressed in terms of normal and tangential traction components acting on a physical plane segment of specified dimension. Mixed-mode conditions are considered for which both critical load value and crack orientation are predicted. The generalized stress intensity factors at the notch tip are determined by applying finite elements accounting for stress singularity. A special device was constructed in order to generate mixed-mode loading conditions in a tensile machine. The experimental program was executed in order to verify predictions of critical load variation and crack orientation for plane notched specimens of polymethyl metacrylate. Experimental data provide satisfactory agreement with model predictions. - See more at: http://ascelibrary.org/doi/abs/10.1061/(ASCE)0733-9399(1997)123%3A6(535)#sthash.M6SKEj2w.dpuf 103 Mróz Z., Giambanco G., An interface model for analysis of deformation behaviour of discontinuities, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/(SICI)1096-9853(199601)20:1<1::AID-NAG799>3.0.CO;2-L, Vol.20, No.1, pp.1-33, 1996Mróz Z., Giambanco G., An interface model for analysis of deformation behaviour of discontinuities, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/(SICI)1096-9853(199601)20:1<1::AID-NAG799>3.0.CO;2-L, Vol.20, No.1, pp.1-33, 1996Abstract:An interface constitutive model is presented accounting for slip and sliding effects and also for dilatancy phenomena. The microslip effects are described by considering spherical asperity interaction with variation of contact area and generation of progressive or reverse slip zones. The incremental constitutive equations are derived with proper memory rules accounting for generation and annihilation of particular slip zones during the process of variable loading. It is further assumed that sliding of spherical contacts occurs along large asperities whose slope varies due to the wear process. The predicted shear and dilatancy curves are shown to provide close quantitative simulation of available experimental data. The strain ratchetting effect for non-symmetric cyclic loading was exhibited using the asperity wear model. The model presented could be applied to simulate rock joints, masonry, or concrete cracked interfaces, under monotonic and cyclic loading. 104 Dems K., Mróz Z., Szolc T., Optimal segmentation of beam and disk structures, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01197041, Vol.11, No.3, pp.252-259, 1996Dems K., Mróz Z., Szolc T., Optimal segmentation of beam and disk structures, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01197041, Vol.11, No.3, pp.252-259, 1996Abstract:Large structures are usually composed of elements by properly designed connections. The optimal design solution in such cases should provide optimal size and number of elements together with optimal connection stiffness. The problem is formulated by assuming the element cost to be a nonlinear function of its size and the cost of connection to depend on its stiffness or transmitted forces. The number of elements and the connection stiffness now constitute the design parameters to be determined. A two-level procedure is proposed for determination of the optimal segmentation for beam and plate structures. Several illustrative examples are presented. 105 Mróz Z., Bojczuk D., Sensitivity Analysis of Truss and Frame Structures in Critical States, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905459608905258, Vol.24, No.1, pp.105-134, 1996Mróz Z., Bojczuk D., Sensitivity Analysis of Truss and Frame Structures in Critical States, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905459608905258, Vol.24, No.1, pp.105-134, 1996Abstract:Truss and frame structures are considered at their critical states, i.e., bifurcation or limit points. When design parameters vary, the critical points evolve and the respective critical loads are modified. This paper is concerned with sensitivity analysis of critical loads with respect to cross-sectional and configuration parameters. The effect of redistribution during the prebuckling state is considered. 106 Seweryn A., Mróz Z., A non-local stress failure condition for structural elements under multiaxial loading, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/0013-7944(94)00335-F, Vol.51, No.6, pp.955-973, 1995Seweryn A., Mróz Z., A non-local stress failure condition for structural elements under multiaxial loading, ENGINEERING FRACTURE MECHANICS, ISSN: 0013-7944, DOI: 10.1016/0013-7944(94)00335-F, Vol.51, No.6, pp.955-973, 1995Abstract:A non-local stress condition for crack initiation and propagation is proposed and applied to several particular cases, such as plate with wedge-shaped notch, elliptical hole and hyperbolic notch. Brittle failure initiation for notched elements under complex loading (Modes I and II) is studied in detail. A value of critical load and crack orientation is predicted from the non-local condition, which is applicable to both regular and singular stress concentrations. 107 Dems K., Mróz Z., Shape sensitivity in mixed Dirichlet-Neumann boundary-value problems and associated class of path-independent integrals, EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, ISSN: 0997-7538, Vol.14, No.2, pp.169-203, 1995Dems K., Mróz Z., Shape sensitivity in mixed Dirichlet-Neumann boundary-value problems and associated class of path-independent integrals, EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, ISSN: 0997-7538, Vol.14, No.2, pp.169-203, 1995Abstract:Considering an arbitrary behavioural functional specified for a mixed Dirichlet-Neumann boundary-value problem, its first variation with respect to variation of domain shape is derived using the material derivative concept and adjoint approach. Next the invariance of this functional is proved for the case of translation, rotation and scale change of an arbitrary homogeneous and isotropic domain of a problem. The associated path-independent integrals are derived and it is shown that the sensitivity analysis with respect to translation, rotation or expansion of defects can be performed by using these integralsKeywords:Numerical method, Boundary-value problems, Path integral, Sensitivity analysis, Holes, Optimization, Geometrical shape 108 Mróz Z., Rodzik P., On the control of deformation process by plastic strain, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/S0749-6419(95)00031-3, Vol.11, No.7, pp.827-842, 1995Mróz Z., Rodzik P., On the control of deformation process by plastic strain, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/S0749-6419(95)00031-3, Vol.11, No.7, pp.827-842, 1995Abstract:The incremental relations are derived between stress rate and the second order plastic strain rate (or plastic strain path curvature). Such relations could be used in setting control of the deformation process by plastic strain either in an experimental test or in numerical procedure, especially when critical and post-critical states occur for stress or strain control. 109 Mróz Z., Stupkiewicz S., An anisotropic friction and wear model, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(94)90167-8, Vol.31, No.8, pp.1113-1131, 1994Mróz Z., Stupkiewicz S., An anisotropic friction and wear model, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(94)90167-8, Vol.31, No.8, pp.1113-1131, 1994Abstract:The classical Coulomb friction condition and the sliding rule are generalized in order to account for friction anisotropy. A model of two surfaces with anisotropic layout of asperities interacting elastically is first considered in order to generate limit friction condition and a sliding rule. Next, a class of phenomenological models is considered in order to simulate anisotropic friction, sliding and wear rate of contacting surfaces. 110 Mróz Z., Design sensitivity analysis of non-linear structures in regular and critical states, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(94)90191-0, Vol.31, No.15, pp.2071-2098, 1994Mróz Z., Design sensitivity analysis of non-linear structures in regular and critical states, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(94)90191-0, Vol.31, No.15, pp.2071-2098, 1994Abstract:A general design sensitivity formulation is introduced for non-linear elastic structures reaching critical equilibrium states. A discretized formulation is considered first and the sensitivity analysis is discussed for regular and critical states including analysis of post-critical behavior. Next, a variational approach is presented for beam and surface structures for which generalized stress and strain operator formulation is applied. The formulae for sensitivity of bifurcation loads are derived in terms of adjoint fields which are shown to be equivalent to post-buckling fields in the case of symmetric bifurcation. 111 Stupkiewicz S., Mróz Z., Elastic beam on a rigid frictional foundation under monotonic and cyclic loading, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(94)90024-8, Vol.31, No.24, pp.3419-3442, 1994Stupkiewicz S., Mróz Z., Elastic beam on a rigid frictional foundation under monotonic and cyclic loading, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(94)90024-8, Vol.31, No.24, pp.3419-3442, 1994Abstract:An elastic beam resting on a frictional foundation and loaded by the concentrated force or moment applied at its tip is considered. The evolution of slip zones along the beam is discussed for both monotonie and cyclic loading. It is shown that an infinite number of slip zones develop and their propagation satisfies in some cases a self-similarity property. Transient hysteretic effects under cyclic loading are discussed. The closed form analytical solution is presented for the elastic friction model in the case of monotonie loading. 112 Mróz Z., Jarzębowski A., Phenomenological model of contact slip, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01178518, Vol.102, No.1, pp.59-72, 1994Mróz Z., Jarzębowski A., Phenomenological model of contact slip, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01178518, Vol.102, No.1, pp.59-72, 1994Abstract:A constitutive model of the contact zone is proposed, accounting for dilatancy, elastic compliance, hardening and softening phenomena, and also hysteresis effects. Some model predictions are discussed in view of available experimental data. 113 Jarzębowski A., Mróz Z., On slip and memory rules in elastic, friction contact problems, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01178527, Vol.102, No.1, pp.199-216, 1994Jarzębowski A., Mróz Z., On slip and memory rules in elastic, friction contact problems, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01178527, Vol.102, No.1, pp.199-216, 1994Abstract:An elastic strip model resting on a frictional plane is first considered in order to illustrate slip and memory rules in the uniaxial case. Next, the axisymmetric slip rules are discussed and referred to the case of slip of two spheres acted on by normal and tangential forces. Close connection to the multisurface hardening plasticity rules is indicated. Slip rules are derived for both proportional and non-proportional loading cases. 114 Bojczuk D., Mróz Z., Sensitivity analysis for non-linear beams and frames, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.32, No.4, pp.867-886, 1994Bojczuk D., Mróz Z., Sensitivity analysis for non-linear beams and frames, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.32, No.4, pp.867-886, 1994Abstract:A geometrically non-linear, elastic frame structure is considered and the effect of small variation of its parameters on structure deformation response is studied. Variations of cross-sectional stiffness, member length, orientation, and also variation of node positions of a discrete structure are considered. The explicit expressions for variation of a displacement functional in terms of primary and adjoint states and of design parameter variations are provided. 115 Li Z.X., Mróz Z., Damage model for viscoplastic-softening behavior: cement paste and concrete, Theoretical and Applied Fracture Mechanics, ISSN: 0167-8442, DOI: 10.1016/0167-8442(94)00005-0, Vol.20, No.2, pp.105-113, 1994Li Z.X., Mróz Z., Damage model for viscoplastic-softening behavior: cement paste and concrete, Theoretical and Applied Fracture Mechanics, ISSN: 0167-8442, DOI: 10.1016/0167-8442(94)00005-0, Vol.20, No.2, pp.105-113, 1994Abstract:A viscoplastic-softening model is developed; it invokes damage accumulation depending on the viscous strain and stress rates. For deformation beyond the peak on the uniaxial stress-strain curve, the softening behavior is modelled by applying the accounting for loss in stiffness due to localized material damage by cracking. Predicted are the hardening/softening behavior of cement paste. The results for applied strain rates of 3 × 10−3, 3 × 10−2 and 3 × 10−1 s−1 agreed well with the test data. Similar success was obtained for the creep of two types of concrete under compression. 116 Dems K., Mróz Z., On shape sensitivity approaches in the numerical analysis of structures, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01743340, Vol.6, No.2, pp.86-93, 1993Dems K., Mróz Z., On shape sensitivity approaches in the numerical analysis of structures, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01743340, Vol.6, No.2, pp.86-93, 1993Abstract:The semi-analytical, analytical and direct methods for numerical structural shape sensitivity analysis are discussed for a beam model and the general three-dimensional case. While the two first methods are applied directly to the finite element model of a structure, the direct approach follows from a continuous formulation and only the final results can be discretized. 117 Dems K., Mróz Z., Shape sensitivity analysis and optimal design of disks and plates with strong discontinuities of kinematic fields, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(92)90209-C, Vol.29, No.4, pp.437-463, 1992Dems K., Mróz Z., Shape sensitivity analysis and optimal design of disks and plates with strong discontinuities of kinematic fields, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(92)90209-C, Vol.29, No.4, pp.437-463, 1992Abstract:Disks, plates or beams subjected to loading and initial strains or displacements are assumed to be composed of portions interconnected by hinge or slip and dilatancy lines admitting discontinuities in displacements or slopes. The shape of such lines and their stiffness properties are subjected to variation. The sensitivity analysis is first discussed for an arbitrary functional of generalized stress, strain, displacement and boundary traction. The variation of complementary and potential energies is considered as a particular case of a general derivation for sensitivity. The optimal design problem is then considered and the relevant optimally conditions are derived. The general theory is illustrated by examples of sensitivity analysis and optimal design with respect to shape, position and stiffness of discontinuity lines for disks, plates and beams. Numerical aspects of sensitivity analysis are also discussed. 118 Mróz Z., Plaut R.H., On the stability and post-critical behavior of elastic structures with dry friction, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(92)90235-L, Vol.29, No.10, pp.1241-1253, 1992Mróz Z., Plaut R.H., On the stability and post-critical behavior of elastic structures with dry friction, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(92)90235-L, Vol.29, No.10, pp.1241-1253, 1992Abstract:The stability of discrete elastic systems subjected to conservative loading is governed by the potential energy, which is a function of the generalized coordinates. When dry friction is present, it affects the stability conditions and the post-critical response. Quasi-static loading is considered and the normal forces to the friction surface are assumed to be specified. General critical state conditions are obtained in terms of the potential energy and the dissipation function. Then several examples are presented to illustrate various types of behavior. It is seen that limit points, bifurcation points, and transition points (associated with slip activation or deactivation) may occur on the deformation path, and that a sudden “snap” from one state to another is a common phenomenon when the system includes dry friction. 119 Plaut R.H., Mróz Z., Uni-directional buckling of a pinned elastica with external pressure, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(92)90196-Z, Vol.29, No.16, pp.2091-2100, 1992Plaut R.H., Mróz Z., Uni-directional buckling of a pinned elastica with external pressure, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(92)90196-Z, Vol.29, No.16, pp.2091-2100, 1992Abstract:Uni-directional buckling of an elastica with pinned ends is investigated. A rigid foundation below the beam prohibits downward deflection, and a uniform pressure acts on the beam from above. The beam weight is neglected and an axial compressive load is applied. Equilibrium paths are determined for various pressures and the effects of initial curvature and load eccentricity are examined. 120 Pycko S., Mróz Z., Alternative approach to shakedown as a solution of a min-max problem, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01182585, Vol.93, No.1, pp.205-222, 1992Pycko S., Mróz Z., Alternative approach to shakedown as a solution of a min-max problem, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01182585, Vol.93, No.1, pp.205-222, 1992Abstract:Melan's classical shakedown theorem for continuous media considered as a problem of methematical programming with constraints is reformulated and reduced to a solution of a certain min-max problem. A similar approach is presented for the structural theory described in terms of generalized variables. A distinction is made between alternating plasticity and incremental collapse modes in the analysis of structures with nonsandwich cross-sections. 121 Trąmpczyński W., Mróz Z., Anisotropic hardening model and its application to cyclic loading, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(92)90043-C, Vol.8, No.8, pp.925-946, 1992Trąmpczyński W., Mróz Z., Anisotropic hardening model and its application to cyclic loading, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(92)90043-C, Vol.8, No.8, pp.925-946, 1992Abstract:The experimental study of evolution rules of two state variables: back street αij and yield stress R are first discussed. It is shown that back stress evolution is affected by the maximal prestress, and asymptotic value of yield stress depends on strain amplitude. The constitutive model is presented next, and its prediction for cyclic loading program is compared with experimental data. 122 Klisiński M., Mróz Z., Runesson K., Structure of constitutive equations in plasticity for different choices of state and control variables, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(92)90049-I, Vol.8, No.3, pp.221-243, 1992Klisiński M., Mróz Z., Runesson K., Structure of constitutive equations in plasticity for different choices of state and control variables, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(92)90049-I, Vol.8, No.3, pp.221-243, 1992Abstract:The structure of incremental equations in plasticity is discussed with respect to the choice of control variables representing stress, strain or mixed control, while (quite independently) the yield surface may be represented in either stress, strain, or mixed space. It is concluded that the choice of state variables does not affect the analytical properties of the resulting equations, whereas the choice of control variables has a major influence on the uniqueness of the stress-strain behaviour. For an associated flow rule the most and least severe restrictions are placed by pure stress control and pure strain control, respectively. 123 Siemaszko A., Mróz Z., Sensitivity of plastic optimal structures to imperfections and non-linear geometrical effects, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/BF01743278, Vol.3, No.2, pp.99-105, 1991Siemaszko A., Mróz Z., Sensitivity of plastic optimal structures to imperfections and non-linear geometrical effects, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615-147X, DOI: 10.1007/BF01743278, Vol.3, No.2, pp.99-105, 1991Abstract:The sensitivity of optimal plastic design with respect to geometric imperfections and post-critical deformations is discussed. It is shown that the concept of optimal plastic design should be modified in order to provide a proper safety factor against collapse for a specified range of imperfections and configuration changes. The optimal design of two-story frames is analysed in detail. 124 Siemaszko A., Mróz Z., Sensitivity of optimal structures to imperfections and non-linear geometrical effects, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01743278, Vol.3, No.2, pp.99-105, 1991Siemaszko A., Mróz Z., Sensitivity of optimal structures to imperfections and non-linear geometrical effects, Structural optimization, ISSN: 0934-4373, DOI: 10.1007/BF01743278, Vol.3, No.2, pp.99-105, 1991Abstract:The sensitivity of optimal plastic design with respect to geometric imperfections and post-critical deformations is discussed. It is shown that the concept of optimal plastic design should be modified in order to provide a proper safety factor against collapse for a specified range of imperfections and configuration changes. The optimal design of two-story frames is analysed in detail. 125 Haftka R.T., Cohen G.A., Mróz Z., Derivatives of Buckling Loads and Vibration Frequencies With Respect to Stiffness and Initial Strain Parameters, JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, ISSN: 0021-8936, DOI: 10.1115/1.2888302, Vol.57, No.1, pp.18-24, 1990Haftka R.T., Cohen G.A., Mróz Z., Derivatives of Buckling Loads and Vibration Frequencies With Respect to Stiffness and Initial Strain Parameters, JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, ISSN: 0021-8936, DOI: 10.1115/1.2888302, Vol.57, No.1, pp.18-24, 1990Abstract:A uniform variational approach to sensitivity analysis of vibration frequencies and bifurcation loads of nonlinear structures is developed. Two methods of calculating the sensitivities of bifurcation buckling loads and vibration frequencies of nonlinear structures, with respect to stiffness and initial strain parameters, are presented. A direct method requires calculation of derivatives of the prebuckling state with respect to these parameters. An adjoint method bypasses the need for these derivatives by using instead the strain field associated with the second-order post-buckling state. An operator notation is used and the derivation is based on the principle of virtual work. The derivative computations are easily implemented in structural analysis programs. This is demonstrated by examples using a general purpose, finite element program and a shell-of-revolution program.Keywords:Oscillating frequencies, Stress, Buckling, Stiffness, Bifurcation, Structural analysis, Computation, Sensitivity analysis, Shells, Virtual work principle 126 Dems K., Mróz Z., Szeląg D., Optimal design of rib-stiffeners in disks and plates, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(89)90017-6, Vol.25, No.9, pp.973-998, 1989Dems K., Mróz Z., Szeląg D., Optimal design of rib-stiffeners in disks and plates, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(89)90017-6, Vol.25, No.9, pp.973-998, 1989Abstract:Disks and plates subjected to stretching and flexure are stiffened by curvilinear ribstiffeners whose shape and cross-sectional area are subject to optimization. Sensitivity analysis is first discussed for an arbitrary integral functional of generalized stress, strain and displacement and boundary domains. The optimality conditions are next derived. The general theory is illustrated by three examples of optimal design of ring-stiffeners in circular disks and plates and of rib-stiffeners in a rectangular plate. 127 Runesson K., Mróz Z., A note on nonassociated plastic flow rules, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(89)90005-3, Vol.5, No.6, pp.639-658, 1989Runesson K., Mróz Z., A note on nonassociated plastic flow rules, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(89)90005-3, Vol.5, No.6, pp.639-658, 1989Abstract:The analytical properties of the constitutive equations in plasticity with a nonassociated flow rule are investigated. Under the assumption of small deformations the directional stiffness (and compliance) rule is considered and the relevant spectral properties of the tangent stiffness tensor are assessed. It is shown that the directional stiffness may be larger than the elastic. It may also be negative in the case of a formally perfectly plastic material and so the nonassociative flow rule represents (spurious) softening in terms of an associated flow rule. The issue of uniqueness at finite strains is briefly addressed, whereby use is made of the tangent stiffness tensor relating the velocity gradient to the first Piola-Kirchhoff stress rate. The relevant spectral properties, which generalise those from the small deformation case, are found explicit. A sufficient condition for uniqueness is given in terms of a critical (upper bound) value of the hardening modulus. 128 Mróz Z., Nawrocki P., Deformation and stability of an elasto-plastic softening pillar, Rock Mechanics and Rock Engineering, ISSN: 0723-2632, DOI: 10.1007/BF01583956, Vol.22, No.2, pp.69-108, 1989Mróz Z., Nawrocki P., Deformation and stability of an elasto-plastic softening pillar, Rock Mechanics and Rock Engineering, ISSN: 0723-2632, DOI: 10.1007/BF01583956, Vol.22, No.2, pp.69-108, 1989Abstract:A model of rock pillar or coal seam is considered assuming linear elastic behaviour before reaching the maximum strength and post-peak behaviour characterized by the residual strength. The deformation and stress across the pillar height are assumed to be uniform and the interaction with overlying rock strata is treated assuming beam model of the strata. The elasto-plastic stress distribution within pillar and the onset of instability occurring for the critical opening span are determined. Comparison with a solution for a simplified “spring” model of pillar is also presented. 129 Mróz Z., Kowalczyk M., Elasto-plastic post-critical analysis of disks under tension, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.41, pp.461-480, 1989 130 Dems K., Mróz Z., Sensitivity of Buckling Load and Vibration Frequency with Respect to Shape of Stiffened and Unstiffened Plates, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/089054508915650, Vol.17, No.4, pp.431-457, 1989Dems K., Mróz Z., Sensitivity of Buckling Load and Vibration Frequency with Respect to Shape of Stiffened and Unstiffened Plates, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/089054508915650, Vol.17, No.4, pp.431-457, 1989Abstract:The method of calculating the sensitivities of buckling loads and vibration frequencies of nonlinear plates with respect to shape functions is presented. These shape functions describe the external shape of an unstiffened plate or the shape of a stiffener within the domain of a plate with fixed external boundaries. An adjoint variable method is used to determine the sensitivities. Thus, only one additional solution for an adjoint plate is required. 131 Mróz Z., Trąmpczyński W., Hayhurst D.R., Anisotropic creep hardening rule for metals and its application to cyclic loading, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(88)90015-0, Vol.4, No.3, pp.279-299, 1988Mróz Z., Trąmpczyński W., Hayhurst D.R., Anisotropic creep hardening rule for metals and its application to cyclic loading, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(88)90015-0, Vol.4, No.3, pp.279-299, 1988Abstract:The creep hardening constitutive model based on the concept of kinematic and isotropic hardening, and the memory of maximal prestress, developed in ́ [1984], is modified and extended in order to increase its simplicity and to describe creep-plasticity interaction programs. Next, the model is applied to the case of cyclic creep deformation in pure copper tubes subjected to combined tension and torsion at 300°C and to cyclic creep of 304 stainless steel at 600°C for varying complex stress levels. 132 Dems K., Mróz Z., Variational approach to sensitivity analysis in thermoelasticity, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495738708927014, Vol.10, No.4, pp.283-306, 1987 133 Dems K., Mróz Z., A Variational Approach to Sensitivity Analysis and Structural Optimization of Plane Arches, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905458708905121, Vol.15, No.3, pp.297-321, 1987Dems K., Mróz Z., A Variational Approach to Sensitivity Analysis and Structural Optimization of Plane Arches, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905458708905121, Vol.15, No.3, pp.297-321, 1987Abstract:A plane arch with variable form or cross-sectional stiffness is considered. The associated variation of any functional that depends on generalized stress, strain, and displacement is explicitly expressed, using primary and adjoint fields. Geometrical linear and material nonlinear behavior of an arch are considered. The optimal design problem is discussed and relevant optimality conditions are derived. Illustrative examples are presented. The analysis presented can be used in optimization of curvilinear stiffeners on disks and plates. 134 Garstecki A., Mróz Z., Optimal Design of Supports of Elastic Structures Subjected to Loads and Initial Distortions, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905458708905108, Vol.15, No.1, pp.47-68, 1987Garstecki A., Mróz Z., Optimal Design of Supports of Elastic Structures Subjected to Loads and Initial Distortions, Mechanics of Structures and Machines, ISSN: 1539-7734, DOI: 10.1080/08905458708905108, Vol.15, No.1, pp.47-68, 1987Abstract:A problem of optimal location, stiffness, and prestress of supports in an elastic frame structure that is subjected to external loads, displacements, and initial distortions is formulated. Sensitivity analysis and optimality conditions are discussed for the assumed objective functional, accounting for conflicting design requirements that correspond to stiffness and stress constraints. A simple example is presented that illustrates the general theory. 135 Dems K., Mróz Z., On a class of conservation rules associated with sensitivity analysis in linear elasticity, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(86)90118-6, Vol.22, No.7, pp.737-758, 1986Dems K., Mróz Z., On a class of conservation rules associated with sensitivity analysis in linear elasticity, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(86)90118-6, Vol.22, No.7, pp.737-758, 1986Abstract:Considering arbitrary stress, strain or displacement functionals specified over a domain of an elastic, homogeneous and isotropic body, their invariance is proved for the case of translation, rotation and scale change of an arbitrary domain within the body. The assosciated class of path-independent integrals is derived. It is shown that sensitivity analysis with respect to translation, rotation or expansion of defects can be performed by using these path-independent integrals. 136 Petryk H., Mróz Z., Time derivatives of integrals and functionals defined on varying volume and surface domains, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.38, No.5-6, pp.697-724, 1986 137 Haftka R., Mróz Z., First- and second-order sensitivity analysis of linear and nonlinearstructures, AIAA Journal, ISSN: 0001-1452, DOI: 10.2514/3.9412, Vol.24, No.7, pp.1187-1192, 1986 138 Dems K., Mróz Z., Variational approach to first- and second-order sensitivity analysis of elastic structures, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620210405, Vol.21, No.4, pp.637-661, 1985Dems K., Mróz Z., Variational approach to first- and second-order sensitivity analysis of elastic structures, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620210405, Vol.21, No.4, pp.637-661, 1985Abstract:For a linear elastic structure, the first variations of arbitrary stress, strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain, in References 1 and 2, by using the solutions for primary and adjoint systems. In this paper, explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters. These expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems. Furthermore, the variation of local stress, strain or displacement is considered. Several illustrative examples are provided for the first- and second-order sensitivity analysis of beams. 139 Mróz Z., Kamat M.P., Plaut R.H., Sensitivity Analysis and Optimal Design of Nonlinear Beams and Plates, Journal of Structural Mechanics, ISSN: 1539-7734, DOI: 10.1080/03601218508907500, Vol.13, No.3-4, pp.245-266, 1985Mróz Z., Kamat M.P., Plaut R.H., Sensitivity Analysis and Optimal Design of Nonlinear Beams and Plates, Journal of Structural Mechanics, ISSN: 1539-7734, DOI: 10.1080/03601218508907500, Vol.13, No.3-4, pp.245-266, 1985Abstract:A uniform formulation of sensitivity analysis for beams and plates is presented in terms of generalized stresses and strains. Both physical and geometric nonlinearities can be treated within this formulation. Next, optimal design problems for stress and deflection constraints are formulated and the relevant optimality conditions are derived using the concept of a linear adjoint structure. Finally, several numerical solutions of optimal design problems of beams are presented. 140 Dems K., Mróz Z., Stability Conditions for Brittle-Plastic Structures with Propagating Damage Surfaces, Journal of Structural Mechanics, ISSN: 1539-7734, DOI: 10.1080/03601218508907492, Vol.13, No.1, pp.95-122, 1985Dems K., Mróz Z., Stability Conditions for Brittle-Plastic Structures with Propagating Damage Surfaces, Journal of Structural Mechanics, ISSN: 1539-7734, DOI: 10.1080/03601218508907492, Vol.13, No.1, pp.95-122, 1985Abstract:The incremental problem for a brittle-plastic body is considered for which stable propagation of a damage interface occurs within the material. The stability conditions are derived and applied to several simple illustrative examples. 141 Mróz Z., In Memory of Professor Antoni Sawczuk, Journal of Structural Mechanics, ISSN: 1539-7734, DOI: 10.1080/03601218508907499, Vol.13, No.3-4, pp.241-243, 1985 142 Mróz Z., Trąmpczyński W., On the creep-hardening rule for metals with a memory of maximal prestress, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(84)90013-1, Vol.20, No.5, pp.467-486, 1984Mróz Z., Trąmpczyński W., On the creep-hardening rule for metals with a memory of maximal prestress, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(84)90013-1, Vol.20, No.5, pp.467-486, 1984Abstract:The creep-hardening constitutive model based on the concept of kinematic hardening is discussed. The distinction is made between active and unloading creep processes and the hardening is assumed to depend on two scalar parameters αm and αn the first representing the maximal prestress measure, the other corresponding to accumulated measure of unloading events. The constitutive model is applied to simulate monotonic and cyclic creep deformation in pure copper tubes subjected to combined tension and torsion at 300°C. The interaction between monotonic and cyclic hardening and the effect of initial prestress are studied and model predictions are compared with experimental data. 143 Dems K., Mróz Z., Variational approach by means of adjoint systems to structural optimization and sensitivity analysis—II: Structure shape variation, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(84)90026-X, Vol.20, No.6, pp.527-552, 1984Dems K., Mróz Z., Variational approach by means of adjoint systems to structural optimization and sensitivity analysis—II: Structure shape variation, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(84)90026-X, Vol.20, No.6, pp.527-552, 1984Abstract:For a linear elastic structure, the first variation of an arbitrary stress, strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems. The application to optimal design is next presented and the relevant optimally conditions are derived from general expressions. The path-independent integrals used in fracture mechanics are rederived as a particular case of general expressions. 144 Dems K., Mróz Z., Variational approach by means of adjoint systems to structural optimization and sensitivity analysis—I: Variation of material parameters within fixed domain, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(83)90064-1, Vol.19, No.8, pp.677-692, 1983Dems K., Mróz Z., Variational approach by means of adjoint systems to structural optimization and sensitivity analysis—I: Variation of material parameters within fixed domain, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(83)90064-1, Vol.19, No.8, pp.677-692, 1983Abstract:For a linear elastic structure, the first variation of an arbitrary stress, strain and displacement functionals corresponding to variation of material parameters within specified domain is derived by using the solution for primary and adjoint systems. This variation is of fundamental importance in sensitivity analysis, optimal design and identification problems. Simple examples of optimal stiffness design and identification of stiffness parameters in beams are presented. 145 Mróz Z., Pietruszczak S., A constitutive model for sand with anisotropic hardening rule, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610070304, Vol.7, No.3, pp.305-320, 1983Mróz Z., Pietruszczak S., A constitutive model for sand with anisotropic hardening rule, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610070304, Vol.7, No.3, pp.305-320, 1983Abstract:An anisotropic hardening model for sand or other granular materials is presented. The state of initial densification is represented by a configuration surface and the state of loading by a loading surface in the stress space. The domain of elastic response may not exist and the irreversible strain is assumed to occur for both active and reverse loading. The derived constitutive equations are applicable both for dense and loose sands. Some model predictions are compared with available experimental data for triaxial compression and extension under undrained condition. 146 Pietruszczak S., Mróz Z., On hardening anisotropy of K0-consolidated clays, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610070105, Vol.7, No.1, pp.19-38, 1983Pietruszczak S., Mróz Z., On hardening anisotropy of K0-consolidated clays, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610070105, Vol.7, No.1, pp.19-38, 1983Abstract:The combined isotropic-kinematic hardening rule for clays is presented using the concept of a multisurface model discussed previously in Reference 1. The mechanical behaviour of clays after one-dimensional consolidation is next simulated for the axisymmetric stress stress state. A general three-dimensional formulation of constitutive relations is also presented. 147 Zubelewicz A., Mróz Z., Numerical simulation of rock burst processes treated as problems of dynamic instability, Rock Mechanics and Rock Engineering, ISSN: 0723-2632, DOI: 10.1007/BF01042360, Vol.16, No.4, pp.253-274, 1983Zubelewicz A., Mróz Z., Numerical simulation of rock burst processes treated as problems of dynamic instability, Rock Mechanics and Rock Engineering, ISSN: 0723-2632, DOI: 10.1007/BF01042360, Vol.16, No.4, pp.253-274, 1983Abstract:The phenomenon of rock burst occurs when the static stability conditions of the rock mass are violated and the dynamic failure process proceeds starting from the equilibrium state. In view of the difficulties in determining numerically the instability point, an alternative approach is advocated here: after solving the initial static problem the mode and onset of dynamic failure are studied by superposition of dynamic disturbances. In this way quantitative analyses of rock burst phenomena may be handled in a relatively simple manner. 148 Lekszycki T., Mróz Z., On Optimal Support Reaction in Viscoelastic Vibrating Structures, Journal of Structural Mechanics, ISSN: 1539-7734, DOI: 10.1080/03601218308907432, Vol.11, No.1, pp.67-79, 1983Lekszycki T., Mróz Z., On Optimal Support Reaction in Viscoelastic Vibrating Structures, Journal of Structural Mechanics, ISSN: 1539-7734, DOI: 10.1080/03601218308907432, Vol.11, No.1, pp.67-79, 1983Abstract:For a viscoelastic beam or frame structure that undergoes forced vibrations, the conditions for optimal support reaction are derived. Translation or rotation of supports are allowed and a functional expressed in terms of stress or strain amplitudes is minimized. Optimality conditions are derived using the concept of an adjoint structure and an illustrative example is presented for the case of beam vibration. 149 Mróz Z., Lekszycki T., Optimal support reaction in elastic frame structures, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/0045-7949(81)90002-X, Vol.14, No.3-4, pp.179-185, 1981Mróz Z., Lekszycki T., Optimal support reaction in elastic frame structures, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/0045-7949(81)90002-X, Vol.14, No.3-4, pp.179-185, 1981Abstract:The conditions for optimal support reaction are derived allowing for translation or rotation of supports and requiring the minimization of global elastic compliance or any other functional of stress or displacements. Two illustrative examples are discussed in detail where besides the optimal solutions, also the sensitivity of design with respect to varying support position and direction is studied. 150 Pietruszczak S., Mróz Z., Finite element analysis of deformation of strain-softening materials, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620170303, Vol.17, No.3, pp.327-334, 1981Pietruszczak S., Mróz Z., Finite element analysis of deformation of strain-softening materials, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620170303, Vol.17, No.3, pp.327-334, 1981Abstract:A finite element analysis of strain-softening materials is presented in which the shear band of prescribed thickness is assumed to exist within elements where maximal stress intensity is reached. The incremental stiffness matrix of the element is derived including shear band deformation. Examples presented in the Paper demonstrate that the load-displacement curve and the displacement field are not sensitive to the mesh size used in the solution. 151 Gierliński J., Mróz Z., Optimal design of elastic plates and beams taking large deflections and shear forces into account, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01173194, Vol.39, No.1, pp.77-92, 1981Gierliński J., Mróz Z., Optimal design of elastic plates and beams taking large deflections and shear forces into account, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01173194, Vol.39, No.1, pp.77-92, 1981Abstract:Large deflections plate theory with shear effects taken into account is first discussed. Next the necessary and sufficient optimality conditions are derived for a mean compliance design when the potential energy is to be maximized with an upper bound imposed on the total structure cost. The strain energy is assumed to depend on a set of design parameters ø representing dimension and configuration variables of cross sectional members. Particular forms of the optimality conditions are discussed for some cases. A specific example of optimal design of a sandwich beam undergoing large deflections is presented in detail. 152 Mróz Z., Sharma K.G., Finite element applications of viscoplasticity with singular yield surfaces, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620150309, Vol.15, No.3, pp.421-436, 1980Mróz Z., Sharma K.G., Finite element applications of viscoplasticity with singular yield surfaces, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620150309, Vol.15, No.3, pp.421-436, 1980Abstract:The side and corner flow rules for viscoplastic materials with singular yield surfaces are discussed and applied in numerical solution of several boundary-value problems. The differences in predictions of displacement and stress fields for different flow rules are demonstrated. 153 Mróz Z., On hypoelasticity and plasticity approaches to constitutive modelling of inelastic behavior of soils, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610040104, Vol.4, No.1, pp.45-55, 1980Mróz Z., On hypoelasticity and plasticity approaches to constitutive modelling of inelastic behavior of soils, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610040104, Vol.4, No.1, pp.45-55, 1980Abstract:A comparative discussion of constitutive rate equations generated by using the hypoelasticity and plasticity theories is presented. If is shown that these two approaches are equivalent for the loading process but differ essentially in defining the unloading (or reverse loading) paths. The multisurface plasticity formulation proves to be more convenient in incorporating memory rules of particular loading events, whereas loading-unloading criteria used in hypoelasticity may result in an unrealistic prediction of material response for some loading paths, and in particular, for cyclic loading. The violation of the continuity condition between loading–unloading domains in proposed constitutive relations3,4 limits their applicability to some particular classes of loading paths. 154 Mróz Z., Mironov A., Optimal design of structures for global mechanical constraints, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.32, No.4, pp.505-516, 1980 155 Kujawski D., Mróz Z., A viscoplastic material model and its application to cyclic loading, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01214633, Vol.36, No.3, pp.213-230, 1980Kujawski D., Mróz Z., A viscoplastic material model and its application to cyclic loading, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01214633, Vol.36, No.3, pp.213-230, 1980Abstract:A kinematic hardening model is generalized by introducing plastic and viscous residual “back” stresses α, β that govern the translation of the yield surface. The evolution equations for α and β are proposed and the material functions are identified for a construction steel by carrying out tension-compression tests at different strain rates. The cyclic tests with changing strain amplitudes and frequencies are next carried out and model predictions are compared with experimental results. 156 Pietruszczak S., Mróz Z., Numerical analysis of elastic-plastic compression of pillars accounting for material hardening and softening, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, ISSN: 1365-1609, DOI: 10.1016/0148-9062(80)91086-4, Vol.17, No.4, pp.199-207, 1980Pietruszczak S., Mróz Z., Numerical analysis of elastic-plastic compression of pillars accounting for material hardening and softening, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, ISSN: 1365-1609, DOI: 10.1016/0148-9062(80)91086-4, Vol.17, No.4, pp.199-207, 1980Abstract:An elastic-plastic model of rock or soil is assumed for which the yield condition depends on hydrostatic pressure and varying material density or porosity. The problem of compression of a finite rectangular pillar between two rigid plates is treated numerically in plane strain conditions by applying the ‘initial stress’ finite element incremental technique. The development of softening and hardening zones within the pillar is studied and related to the load carrying capacity of the pillar. 157 Szeląg D., Mróz Z., Optimal design of vibrating beams with unspecified support reactions, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/0045-7825(79)90063-X, Vol.19, No.3, pp.333-349, 1979Szeląg D., Mróz Z., Optimal design of vibrating beams with unspecified support reactions, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/0045-7825(79)90063-X, Vol.19, No.3, pp.333-349, 1979Abstract:The optimal design problem concerns vibrating beams having unspecified thicknesses and lengths as well as supports whose positions and stiffnesses are to be determined. The character of optimal solutions is discussed, and it is shown that the optimal support position may correspond to unimodal or multimodal vibrating states. An iterative design procedure is discussed and applied to generate optimal designs in simple cases. Optimal design for more complex cases can be achieved by proper scaling and connecting basic solutions. 158 Masur E.F., Mróz Z., Non-stationary optimality conditions in structural design, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(79)90051-9, Vol.15, No.6, pp.503-512, 1979Masur E.F., Mróz Z., Non-stationary optimality conditions in structural design, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(79)90051-9, Vol.15, No.6, pp.503-512, 1979Abstract:In some cases, optimal structural design corresponds to non-analytical points for which the first variation of volume or cost does not necessarily vanish. Such cases may occur, for instance, when optimal design is aimed at maximizing the lowest eigenvalue (natural frequency, buckling load) and a multimodal solution occurs, or when the aim is to minimize the maximum stress intensity. The present paper discusses such cases and provides the relevant optimality conditions. 159 Mróz Z., Shamijev F.G., Simplified yield conditions for fibre-reinforced plates and shells, ARCHIVES OF CIVIL ENGINEERING, ISSN: 1230-2945, Vol.25, No.3, pp.463-476, 1979 160 Dragon A., Mróz Z., A continuum model for plastic-brittle behaviour of rock and concrete, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(79)90058-2, Vol.17, No.2, pp.121-137, 1979Dragon A., Mróz Z., A continuum model for plastic-brittle behaviour of rock and concrete, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(79)90058-2, Vol.17, No.2, pp.121-137, 1979Abstract:The present work deals with a continuum model for time-independent behaviour of progressively fracturing solids. The rate theory with fracture parameter is discussed and applied to rock-like materials. In particular, elastic-brittle and plastic-brittle idealizations are considered with the fracturing affecting elastic and plastic strains, respectively. The elastic-brittle model incorporates, however, the plasticity-like concept of varying fracture surface. Also the idea of a limit (failure) locus is introduced as the stress-path dependent condition, instead of being prescribed a priori. The plasticity model attempts to cover both stable and unstable portions of the stress-strain relation while the fracture parameter is coupled with irreversible volumetric dilatancy. The general model is applicable to wider class of engineering materials, ƒ. ex. to metals in advanced yielding accompanied with microfracturing. 161 Dragon A., Mróz Z., A model for plastic creep of rock-like materials accounting for the kinetics of fracture, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, ISSN: 1365-1609, DOI: 10.1016/0148-9062(79)91200-2, Vol.16, No.4, pp.253-259, 1979Dragon A., Mróz Z., A model for plastic creep of rock-like materials accounting for the kinetics of fracture, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, ISSN: 1365-1609, DOI: 10.1016/0148-9062(79)91200-2, Vol.16, No.4, pp.253-259, 1979Abstract:The constant stress creep behaviour of rocks is studied. A model is presented employing assumption that time-dependent microcracking is responsible for the macroscopic viscoplastic deformation. Irreversible volumetric creep is included as the main concern is the material behaviour for stress-levels over the ‘discontinuity’ locus which is identified with the initial yield point. A modified formalism of plasticity theory is used with a scalar crack-density parameter. The steady-state and tertiary creep stages (up to failure) are described by the simplified theory. identification of material parameters is discussed and an example of creep curves for the case of homogeneous biaxial compression is given to illustrate applicability of the model. 162 Dems K., Mróz Z., Multiparameter structural shape optimization by the finite element method, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620130204, Vol.13, No.2, pp.247-263, 1978Dems K., Mróz Z., Multiparameter structural shape optimization by the finite element method, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1620130204, Vol.13, No.2, pp.247-263, 1978Abstract:The problem of optimal design of the shape of a free or internal boundary of a body is formulated by assuming the boundary shape is described by a set of prescribed shape functions and a set of shape parameters. The optimzation procedure is reduced to determination of these paramenters. For constant volume or material cost constraint, the optimality conditions are derived for the case of mean complicance design of elastic structures of a non-linear material. Some additional conditions for the global minimum of the mean compliance are proved. The most typical cases of boundary variations are discussed. The optimal shape problem is next formulated by means of the finite element method and the iterative solution algorithm is discussed by using the optimalitycriteria. Several simple numerical examples are included. 163 Lepik Ü., Mróz Z., Optimal design of impulsively loaded plastic beams for asymmetric mode motions, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(78)90074-4, Vol.14, No.10, pp.841-850, 1978Lepik Ü., Mróz Z., Optimal design of impulsively loaded plastic beams for asymmetric mode motions, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(78)90074-4, Vol.14, No.10, pp.841-850, 1978Abstract:Optimal design of a rigid-plastic stepped beam is discussed assuming the mode form of motion. Such beam dimensions are sought for which a minimum of local or mean deflection is attained within designs of constant volume. It is assumed that the prescribed kinetic energy is imparted to the structure at the initial instant with free motion occurring afterwards. It is shown that besides three symmetric modes of motion, also the asymmetric modes may exist. An optimal design for asymmetric modes is determined and compared with a respective design for symmetric modes, obtained previously in [1]. 164 Mróz Z., Norris V.A., Zienkiewicz O.C., An anisotropic hardening model for soils and its application to cyclic loading, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610020303, Vol.2, No.3, pp.203-221, 1978Mróz Z., Norris V.A., Zienkiewicz O.C., An anisotropic hardening model for soils and its application to cyclic loading, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 0363-9061, DOI: 10.1002/nag.1610020303, Vol.2, No.3, pp.203-221, 1978Abstract:An anisotropic hardening model for soils is proposed by applying the concept of a field of hardening moduli developed previously for metals. Besides the yield surface, a set of nesting surfaces in the stress-space specifies the variation of hardening moduli during the deformation process. Both drained and undrained soil behaviour can be treated and distortional as well as volumetric strain cycles can be considered. The model can be applied in studying soil behaviour under cyclic loading and in particular to describe densification or liquefaction phenomena. 165 Szeląg D., Mróz Z., Optimal Design of Elastic Beams with Unspecified Support Conditions, ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 0044-2267, DOI: 10.1002/zamm.19780581105, Vol.58, No.11, pp.501-510, 1978Szeląg D., Mróz Z., Optimal Design of Elastic Beams with Unspecified Support Conditions, ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 0044-2267, DOI: 10.1002/zamm.19780581105, Vol.58, No.11, pp.501-510, 1978Abstract:Formulation of the problem of optimal design for beams with unspecified support position and stiffness is presented. It is assumed that the beam is composed of segments of unspecified cross-sections and lengths which are to be determined together with support positions and cross-sections. Design for specified mean compliance, first frequency of free vibrations or buckling force is considered and proper optimality criteria are derived. Illustrative examples are presented and the iterative algorithm of numerical solution is discussed in detail. 166 Michałowski R., Mróz Z., Associated and non-associated sliding rules in contact friction problems, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.3, pp.259-276, 1978 167 Lepik Ü., Mróz Z., Optimal design of plastic structures under impulsive and dynamic pressure loading, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(77)90048-8, Vol.13, No.7, pp.657-674, 1977Lepik Ü., Mróz Z., Optimal design of plastic structures under impulsive and dynamic pressure loading, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(77)90048-8, Vol.13, No.7, pp.657-674, 1977Abstract:Optimal design of a rigid-plastic stepped beam and circular plate is considered in the first part of the paper assuming the mode form of motion. The form of optimal mode is sought for which a structure of constant volume attains a minimum of local or mean deflection. It is assumed that the constant kinetic energy Ko is attained by the structure through impulsive loading. Differences between optimal static and dynamic solutions are discussed. Non-uniqueness of modes is demonstrated and significance of stable mode motions is emphasized. In the second part of the paper, an optimal design of a rigid-plastic stepped beam loaded by a uniform pressure over a time interval 0 ⩽ t ⩽ t1 is considered assuming constant beam volume and looking for a design corresponding to minimum of local deflection. The solution presented is valid for moderate dynamic pressures when mode motion occurs during consecutive time intervals and no travelling plastic hinges exist. 168 Fryze W., Mróz Z., Yield conditions of fiber-reinforced materials, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867-888X, Vol.25, pp.201-234, 1977 169 Mróz Z., Pietruszczak S., Description of polymer impregnated concrete, ARCHIVES OF CIVIL ENGINEERING, ISSN: 1230-2945, Vol.23, pp.107-124, 1977 170 Mróz Z., Pietruszczak S., Flexure and extension of concrete beams with polymer impregnated external layers, ARCHIVES OF CIVIL ENGINEERING, ISSN: 1230-2945, Vol.23, pp.125-144, 1977 171 Mróz Z., Shrivastava H.P., Dubey R.N., A non-linear hardening model and its application to cyclic loading, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01176929, Vol.25, No.1, pp.51-61, 1976Mróz Z., Shrivastava H.P., Dubey R.N., A non-linear hardening model and its application to cyclic loading, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01176929, Vol.25, No.1, pp.51-61, 1976Abstract:By modifying the translational rule in a non-linear, kinematic hardening model, it is shown that some phenomena occuring during cyclic loading can be simulated: stress relaxation for cycles with prescribed strain amplitude superposed upon fixed strain, axial strain accumulation for asymetric stress cycle, cyclic hardening or softening. It is also shown that the variation of hardening modulus along the yield surface after plastic prestrain is fairly well described by the present model. The accumulation and relaxation phenomena depend on additional material function which can be determined from uniaxial loading-unloading or cyclic loading tests. 172 Grzymkowski M., Mróz Z., Slip-line solutions of axisymmetric problems of plate compression, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867-888X, Vol.24, pp.171-183, 1976 173 Dragon A., Mróz Z., On the plastic-brittle behaviour of rock and concrete, Mechanics Research Communications, ISSN: 0093-6413, DOI: 10.1016/0093-6413(76)90106-3, Vol.3, No.5, pp.429-434, 1976 174 Mróz Z., Raniecki B., A derivation of the uniqueness conditions in coupled thermoplasticity, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(76)90012-4, Vol.14, No.4, pp.395-401, 1976Mróz Z., Raniecki B., A derivation of the uniqueness conditions in coupled thermoplasticity, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(76)90012-4, Vol.14, No.4, pp.395-401, 1976Abstract:This article presents the proof of local and global uniqueness conditions in rate independent coupled thermoplasticity. The mathematical structure of rate equations which account for all coupling effects was discussed in [1] where uniqueness conditions were stated without proof and discussed for some particular cases. 175 Mróz Z., Raniecki B., On the uniqueness problem in coupled thermoplasticity, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(76)90090-2, Vol.14, No.2, pp.211-221, 1976Mróz Z., Raniecki B., On the uniqueness problem in coupled thermoplasticity, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(76)90090-2, Vol.14, No.2, pp.211-221, 1976Abstract:Rate equations of coupled thermoplasticity are derived assuming that the total strain rate is composed of elastic and plastic terms and accounting for coupling effects such as heat of dissipation, piezocaloric effect, in both mechanical and temperature equations. Local and global uniqueness conditions are presented and its engineering significance is discussed. 176 Mróz Z., Garstecki A., Optimal design of structures with unspecified loading distribution, Journal of Optimization Theory and Applications, ISSN: 0022-3239, DOI: 10.1007/BF00933629, Vol.20, No.3, pp.359-380, 1976Mróz Z., Garstecki A., Optimal design of structures with unspecified loading distribution, Journal of Optimization Theory and Applications, ISSN: 0022-3239, DOI: 10.1007/BF00933629, Vol.20, No.3, pp.359-380, 1976Abstract:The problem of the optimal distribution of loading on a structure that corresponds to the minimum of the elastic compliance or the maximum of the safety factor for plastic collapse is considered. Optimality criteria are derived, and their applicability is illustrated in the case of beams. Besides the optimally varying cross section, also the support positions and the load distribution are determined from the optimal solution.Keywords:Structural optimization, engineering design, optimality conditions, calculus of variations, structural mechanics 177 Mróz Z., Lind N.C., Simplified theories of cyclic plasticity, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01170622, Vol.22, No.1, pp.131-152, 1975Mróz Z., Lind N.C., Simplified theories of cyclic plasticity, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01170622, Vol.22, No.1, pp.131-152, 1975Abstract:Simple theories of plasticity such as flow rules associated with a single yield surface are sufficiently accurate in predicting plastic behaviour for monotonic loading. However, for alternating or cyclic loads, such theories cannot describe complex plastic behaviour with sufficient accuracy. The concept of multiple loading surfaces or internal state parameters may then be introduced and respective plasticity theories become considerably complicated, requiring step by step integration of incremental relations for both strain and internal parameters. The present paper is aimed at elaborating relatively simple models of cyclic behaviour that could be expressed in terms of generalized stresses and strains and could be applied in treating boundary-value problems for beams, plates and shells. Finite stress-strain relations are derived in several subdomains of the stress space, both for loading, unloading and subsequent loading conditions. It is assumed that a set of discrete points from the past history affects the actual state. Some particular cases of cyclic loading of a tube and circular plates are considered in detail in order to illustrate applicability of proposed description. 178 Mróz Z., Rozvany G.I.N., Optimal design of structures with variable support conditions, Journal of Optimization Theory and Applications, ISSN: 0022-3239, DOI: 10.1007/BF00933023, Vol.15, No.1, pp.85-101, 1975Mróz Z., Rozvany G.I.N., Optimal design of structures with variable support conditions, Journal of Optimization Theory and Applications, ISSN: 0022-3239, DOI: 10.1007/BF00933023, Vol.15, No.1, pp.85-101, 1975Abstract:The conditions for optimal location of supports are derived for the case of elastic design for specified mean compliance and plastic design for given safety factor of plastic collapse. The optimal design problem is next formulated including position-dependent cost of support into the design procedure. Both rigid and flexible or yielding supports are considered.Keywords:Structural optimization, engineering design, optimality conditions, calculus of variations, structural mechanics 179 Mróz Z., Taylor J.E., Prestress for maximum strength, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(73)90058-9, Vol.9, No.12, pp.1535-1541, 1973Mróz Z., Taylor J.E., Prestress for maximum strength, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(73)90058-9, Vol.9, No.12, pp.1535-1541, 1973Abstract:The problem of designing prestress to maximize elastic capacity is treated analytically. Our formulation models structures comprised of a one-material elastic continuum, subject to a single deterministic load configuration. The equations needed to predict the optimal prestress design are derived. They are shown to comprise necessary and sufficient conditions for global maximum strength in the unconstrained design problem. The theory is demonstrated on the design of prestress for a thick-walled cylinder. 180 Shrivastava H.P., Mróz Z., Dubey R.N., Yield criterion and second-order effects in plane-stress, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01260885, Vol.17, No.1, pp.137-143, 1973Shrivastava H.P., Mróz Z., Dubey R.N., Yield criterion and second-order effects in plane-stress, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01260885, Vol.17, No.1, pp.137-143, 1973Abstract:A yield criterion in planestress state is derived here based on isotropic representation of a scalar valued function depending upon symmetric 2×2 stress and strain matrices. The material has been assumed to be incompressible. In particular, for tension-torsion loading the yield surface is nonsymmetric with respect to the torsional stress axis. Due to the non-symmetry, the yield condition describes the second-order effect relating to axial-strain accumulation in cyclic torsion, and at the same time it has got a very simple form compared to other yield conditions describing this effect. 181 Mróz Z., Raniecki B., Variational principles in uncoupled thermoplasticity, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(73)90080-3, Vol.11, No.11, pp.1133-1141, 1973Mróz Z., Raniecki B., Variational principles in uncoupled thermoplasticity, International Journal of Engineering Science, ISSN: 0020-7225, DOI: 10.1016/0020-7225(73)90080-3, Vol.11, No.11, pp.1133-1141, 1973Abstract:Stress-rate and strain-rate variational principles are derived for a viscoplastic material characterized by additive elastic and inelastic strain rates. Elastic, viscous and plastic properties are assumed to be temperature dependent but all coupling effects are neglected. 182 Mróz Z., Goss Cz., O złożonych modelach wzmocnienia plastycznego, Mechanika Teoretyczna i Stosowana, ISSN: 0079-3701, Vol.2, No.10, pp.259-279, 1972 183 Mróz Z., Kwaszczyńska K., Some boundary value problems for density hardening materials, Rozprawy Inżynierskie, ISSN: 0867-888X, Vol.19, pp.15-42, 1971 184 Mróz Z., Szymański Cz., A simplified theory of flow of granular materials in converging channels, Archiwum Inżynierii Lądowej, ISSN: 1230-2945, Vol.17, pp.555-578, 1971 185 Kozłowski W., Mróz Z., Optimal design of disks subject to geometric constraints, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/0020-7403(70)90029-9, Vol.12, No.12, pp.1007-1021, 1970Kozłowski W., Mróz Z., Optimal design of disks subject to geometric constraints, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/0020-7403(70)90029-9, Vol.12, No.12, pp.1007-1021, 1970Abstract:A general formulation of the problem of optimal design with geometric constraints is presented. Such constraints define an admissible region in which the variable portion of a structure should be placed. The optimal design of perfectly plastic disks of Tresca material is considered and two problems are discussed in detail: a disk simply supported at two points supports and a cantilever disk loaded by a concentrated force. The optimal design lies in the semi-plane below the line joining supports or within a strip of prescribed width. 186 Mróz Z., Optimal design of structures of composite materials, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(70)90001-6, Vol.6, No.7, pp.859-870, 1970Mróz Z., Optimal design of structures of composite materials, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(70)90001-6, Vol.6, No.7, pp.859-870, 1970Abstract:Optimal design criteria for structures of composite materials are discussed assuming that the phases are either perfectly plastic or perfectly elastic and the design is aimed at maximizing limit load or minimizing static compliance of the structure. Both internal and external reinforcement are considered. An example of a circular plate is presented in order to illustrate the general criteria. 187 Mróz Z., Optimal Design of Elastic Structures Subjected to Dynamic, Harmonically-Varying Loads, ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 0044-2267, DOI: 10.1002/zamm.19700500505, Vol.50, No.5, pp.303-309, 1970Mróz Z., Optimal Design of Elastic Structures Subjected to Dynamic, Harmonically-Varying Loads, ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 0044-2267, DOI: 10.1002/zamm.19700500505, Vol.50, No.5, pp.303-309, 1970Abstract:Optimal design of elastic structures subjected to one or several dynamic, harmonically-varying load systems is discussed assuming the notion of dynamic stiffness as the design criterion. A generalized variational principle is used in deriving the necessary and sufficient conditions of optimal design. Sandwich and solid beams and plates are discussed and the difference of formulation of optimization problem for sandwich and solid sections is emphasized. The method of perturbation is applied to solve particular boundary-value problems. 188 Kwaszczyńska K., Mróz Z., Drescher A., Analysis of compression of short cylinders of Coulomb material, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/0020-7403(69)90001-0, Vol.11, No.2, pp.145-158, 1969Kwaszczyńska K., Mróz Z., Drescher A., Analysis of compression of short cylinders of Coulomb material, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/0020-7403(69)90001-0, Vol.11, No.2, pp.145-158, 1969Abstract:A static solution is presented for the case of compression of short circular cylinders between rough, rigid plates. It is assumed that the material is perfectly plastic, satisfying the Coulomb yield condition and the associated flow law. The stress state is calculated for the edge régime of the Coulomb hexagon for which the Haar-Kármán hypothesis is satisfied. The solution is obtained for several height-diameter ratios, various friction conditions at the cylinder-plate interface and for various angles of internal friction. Results of theoretical solutions are compared with available experimental data. The analysis may be useful in experimental determination of the angle of internal friction and cohesion by compressing short cylinders between rigid plates. 189 Kozłowski W., Mróz Z., Optimal design of solid plates, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(69)90045-6, Vol.5, No.8, pp.781-794, 1969Kozłowski W., Mróz Z., Optimal design of solid plates, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(69)90045-6, Vol.5, No.8, pp.781-794, 1969Abstract:The problem of optimal design of solid plates is concerned with the determination of a variable plate thickness that corresponds to minimum volume when the limit load is prescribed. In its solution, the condition of constancy of specific power of dissipation on the exterior plate surfaces is usually applied. This condition only assures a stationary value of the volume and may represent neither an absolute nor a local minimum. Examples of cantilever and circular plates are discussed, and alternative designs are presented which are of smaller volumes than the usual design. A modified formulation of the optimal design problem is discussed. 190 Mróz Z., Drescher A., Limit Plasticity Approach to Some Cases of Flow of Bulk Solids, Journal of Engineering for Industry, ISSN: 0022-1817, DOI: 10.1115/1.3591573, Vol.91, No.2, pp.357-364, 1969Mróz Z., Drescher A., Limit Plasticity Approach to Some Cases of Flow of Bulk Solids, Journal of Engineering for Industry, ISSN: 0022-1817, DOI: 10.1115/1.3591573, Vol.91, No.2, pp.357-364, 1969Abstract:Depending on the stress state, a bulk solid, regarded as the elastic-plastic material, can exhibit workhardening, worksoftening or perfectly plastic properties. During continuing motion, the solid flow can be assumed as incompressible, and the stress field satisfies a condition of critical state which can be identified with the Coulomb yield condition. The model of Coulomb material is introduced; such material satisfies the Coulomb yield condition and the flow law associated with this condition by the plastic potential rule. In general, the Coulomb material is stronger than the considered bulk solid in the critical state. The kinematic approach and the familiar upper bound theorem are applied in order to determine lower bounds on pressure exerted by the flowing material on bin walls and to determine flowability criterion. In the latter section, the flow induced by a horizontally moving rough plate is analyzed and two flow patterns are considered.Keywords:Flow (Dynamics), Plasticity, Bulk solids, Coulombs, Critical points (Physics), Stress, Surface roughness, Motion, Theorems (Mathematics), Pressure 191 Mróz Z., An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model, TRIBOLOGY LETTERS, ISSN: 1023-8883, DOI: 10.1007/BF01176668, Vol.7, No.2, pp.199-212, 1969Mróz Z., An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model, TRIBOLOGY LETTERS, ISSN: 1023-8883, DOI: 10.1007/BF01176668, Vol.7, No.2, pp.199-212, 1969Abstract:In many problems of plastic deformation, when the prescribed loads or displacement do not increase in proportion but vary in a complex manner, for instance alternating between prescribed limits, more general work-hardening models are needed in order to describe the plastic behavior. One of such models, previously proposed by the author, is applied here in order to discuss superposition of fixed and alternating loads. In particular, the case of steady tension and alternating torsion is considered in detail and the rate of axial strain accumulation is computed. There is a qualitative aggreement between theoretical prediction and experimental data. 192 Mróz Z., Kwaszczyńska K., Axially symmetric plastic flow of metals treated by the graphical methods, Archiwum Inżynierii Lądowej, ISSN: 1230-2945, Vol.14, pp.27-37, 1968 193 Mróz Z., On the description of anisotropic workhardening, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 0022-5096, DOI: 10.1016/0022-5096(67)90030-0, Vol.15, No.3, pp.163-175, 1967Mróz Z., On the description of anisotropic workhardening, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 0022-5096, DOI: 10.1016/0022-5096(67)90030-0, Vol.15, No.3, pp.163-175, 1967Abstract:A model of workhardening is proposed which generalizes the known rules of isotropic and kinematic workhardening by introducing the concept of a ‘field of workhardening moduli.’ This field is defined by a configuration of surfaces of constant workhardening moduli in the stress space. For any loading history the instantaneous configuration can be determined by calculating the translation and expansion or contraction of all surfaces; the material behaviour can thus be determined for complex loading paths, in particular for cyclic loadings. Several examples for a plane stress state are presented. 194 Mróz Z., Graphical solution of axially symmetric problems of plastic flow, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, ISSN: 0044-2275, DOI: 10.1007/BF01596914, Vol.18, No.2, pp.219-236, 1967Mróz Z., Graphical solution of axially symmetric problems of plastic flow, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, ISSN: 0044-2275, DOI: 10.1007/BF01596914, Vol.18, No.2, pp.219-236, 1967Abstract:Une méthode graphique de solution des problèmes dans le cas de symétrie axiale a été proposée pour des corps rigides, parfaitement plastiques, obéissants au critère d'écoulement de Coulomb-Tresca et à l'hypothèse du potentiel plastique. Deux cas ont été considérés: d'une part des régimes de Haar-Kármán pour lesquels la contrainte circonférencielle est égale à l'une des contraintes principales contenues dans le plan axial, et d'autre part des régimes duor lesquels l'une des vitesses de déformation principales dans le plan axial est nulle. 195 Mróz Z., Kwaszczyńska K., Plastic compression of short cylinders between rigid plates, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.19, 1967 196 Drescher A., Kwaszczyńska K., Mróz Z., Statics and kinematics of the granular medium in the case of wedge indentation, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.19, pp.99-113, 1967 197 Mróz Z., On the optimum design of reinforced slabs, TRIBOLOGY LETTERS, ISSN: 1023-8883, DOI: 10.1007/BF01193599, Vol.3, No.1, pp.34-55, 1967Mróz Z., On the optimum design of reinforced slabs, TRIBOLOGY LETTERS, ISSN: 1023-8883, DOI: 10.1007/BF01193599, Vol.3, No.1, pp.34-55, 1967Abstract:A problem of optimum design of reinforced slabs is analyzed assuming a rigid, perfectly-plastic model of both concrete and reinforcement. For a slab of constant thickness such static field is sought which minimizes the total amount of reinforcement under constant limit load; for a slab of varying thickness, the total cost of materials is assumed as a design criterion. Two approximations of the nonlinear cost function are introduced and the corresponding static and kinematic relations are discussed in detail. Several examples of circular and annular slabs under symmetric and non-symmetric loading are considered in order to illustrate the theory. 198 Mróz Z., On forms of constitutive laws for elastic-plastic solids, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.18, No.1, pp.3-35, 1966 199 Mróz Z., Admissible loading paths in the deformation theories of plasticity, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.16, 1964 200 Mróz Z., Bing-ye X., The load carrying capacities of symmetrically loaded spherical shells, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.15, pp.245-266, 1963 201 Mróz Z., Limit analysis of plastic structures subject to boundary variations, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, No.15, pp.63-76, 1963 202 Mróz Z., Non-associated flow laws in plasticity, Journal de mécanique, ISSN: 0021-7832, Vol.2, pp.21-42, 1963 203 Mróz Z., On a problem of minimum weight design, Quarterly of Applied Mathematics, ISSN: 1552-4485, DOI: 10.1090/qam/135327, Vol.19, pp.127-135, 1961Mróz Z., On a problem of minimum weight design, Quarterly of Applied Mathematics, ISSN: 1552-4485, DOI: 10.1090/qam/135327, Vol.19, pp.127-135, 1961Abstract:A problem of optimal design for perfectly plastic, isotropic structures is analyzed. It is shown that for such structures as plates or shells, an extremum of the volume, if it exists, is either a local maximum or a minimum. 204 Mróz Z., The load-carrying capacity of orthotropic shells, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.12, pp.85-107, 1960 205 Mróz Z., Plastic deformation of annular plates under dynanic loads, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.10, pp.499-516, 1958 206 Olszak W., Mróz Z., Note on the completeness of elastic-plastic solution to certain boundary-value problems for the eccentric ring, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.10, pp.441-444, 1958 207 Mróz Z., The load carrying capacity and minimum weight design of annular plates, Rozprawy Inżynierskie, ISSN: 0867-888X, Vol.4, pp.605-625, 1958 208 Mróz Z., Limit analysis and optimal design of annular plates, Rozprawy Inżynierskie, ISSN: 0867-888X, pp.605-626, 1958 209 Olszak W., Mróz Z., Elastic bending of circular plates with eccentric holes /application of the method of inversion/, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 0373-2029, Vol.9, No.125, pp.153, 1957

##### Lista ostatnich monografii
 1.542 Derski W., Izbicki R., Kisiel I., Mróz Z., Rock and Soil Mechanics, PWN, Elsevier Science, series Geotechnical Engineering and Engineering Geology, 48, pp.1-720, 1989 2.29 Derski W., Izbicki R., Kisiel I., Mróz Z., Mechanika skał i gruntów, PWN, Seria Mechanika Techniczna, t. 7, pp.1-573, 1982
##### Lista rozdziałów w ostatnich monografiach
 1.544 Mróz Z., Reference Module in Materials Science and Materials Engineering, rozdział: Strength Theories, Elsevier B.V. (Update of Mróz Z., Comprehensive Structural Integrity, 2.01 - Strength Theories, Elsevier B.V., 2: Fundamental Theories and Mechanisms of Failure, pp.1-46, 2003), pp.1-46, 2017 2.521 Mróz Z., Seweryn A., Advances in Shape Memory Materials, In Commemoration of the Retirement of Profesor Hisaaki Tobushi, rozdział: Thermomechanical Coupling and Localization Effects Examined in Shape Memory Alloys and Polymers by Fast and Sensitive Infrared Camera, Springer International Publishing, series Advanced Structured Materials, 73, pp.173-189, 2017 3.431 Páczelt I., Baksa A., Mróz Z., Mathematical Modeling and Optimization of Complex Structures, Computational Methods in Applied Sciences, rozdział: Contact Optimization Problems for Stationary and Sliding Conditions, Springer, 40, pp.281-312, 2016 4.519 Dems K., Mróz Z., Tofil S., Antoszewski B., Wybrane Problemy w Mechatronice i Inżynierii Materiałowej, MONOGRAFIE, STUDIA, ROZPRAWY, rozdział: Wpływ parametrów spawania laserowego na właściwości złącza Ni-Pt w świecach zapłonowych w silnikach na biopaliwo, Politechnika Świętokrzyska, Kielce, pp.22-33, 2016 5.538 Dems K., Mróz Z., Encyclopedia of Thermal Stresses, rozdział: Sensitivity Analysis for Thermoelastic State Fields, Springer Netherlands, pp.4290-4300, 2014 6.279 Maciejewski J., Białas M., Mróz Z., 6th European Congress on Computational Methods in Applied Sc. and Engng. (ECCOMAS 2012), September 10-14, 2012, Vienna, Austria, rozdział: Modelling of contact interface oxidation process at asperity scale, University of Vienna, Austria, pp.1-8, 2012 7.4 Mróz Z., Maciejewski J., Bifurcations, Instabilities and Degradations in Geomaterials, rozdział: Critical Plane Approach to Analysis of Failure Criteria for Anisotropic Geomaterials, Springer-Verlag Berlin Heidelberg, pp.69-89, 2011 8.41 Maciejewski J., Mróz Z., Bifurcations, Instabilities and Degradations in Geomaterials, rozdział: Analysis of Deformation and Damage Processes in Soil-Tool Interaction Problems, Springer-Verlag Berlin Heidelberg, pp.325-345, 2011 9.176 Białas M., Mróz Z., Multiscale modelling of damage and fracture processes in composite materials, Series: CISM International Centre for Mechanical Sciences, rozdział: Damage models at material interfaces, Springer, Sadowski T. (Ed.), 474, pp.213-270, 2005 10.18 Mróz Z., Dems K., Parameter Identification of Materials and Structures, CISM International Centre for Mechanical Sciences, rozdział: Identification of damage in beam and plate structures using parameter dependent modal changes and thermographic methods, Springer, Mróz Z., Stavroulakis G.E. (Eds.), 469, pp.95-139, 2005 11.545 Mróz Z., Comprehensive Structural Integrity, rozdział: 2.01 - Strength Theories, Elsevier B.V., 2: Fundamental Theories and Mechanisms of Failure, pp.1-46, 2003 12.536 Mróz Z., Friction and Instabilities, rozdział: Contact Friction Models and Stability Problems, Springer Vienna, series International Centre for Mechanical Sciences, 457, pp.179-232, 2002 13.525 Mróz Z., Białas M., IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials, rozdział: Modeling of Progressive Interface Failure Under Monotonic and Cyclic Loading, Springer, Dordrecht, series Solid Mechanics and its Applications, 97, pp.211-222, 2002 14.526 Sadowski T., Samborski S., Mróz Z., IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials, rozdział: Gradual Degradation of Initially Porous Polycrystalline Ceramics Subjected to Quasi-Static Tension, Springer, Dordrecht, series Solid Mechanics and its Applications, 97, pp.401-405, 2002 15.527 Stupkiewicz S., Mróz Z., Contact Mechanics, rozdział: Phenomenological Model of Friction Accounting for Subsurface Plastic Deformation in Metal Forming, Springer Netherlands, series Solid Mechanics and Its Applications, 103, pp.179-186, 2002 16.523 Mróz Z., Stupkiewicz S., IUTAM Symposium on Micro- and Macrostructural Aspects of Thermoplasticity, rozdział: Thermoplastic Deformation at Interfaces in Metal Forming Processes, Kluwer Academic Publishers, series Solid Mechanics and its Applications, 62, pp.489-498, 1999 17.541 Mróz Z., Seweryn A., Damage Mechanics in Engineering Materials, rozdział: Damage evolution rule for multiaxial variable loading, Elsevier, series Studies in Applied Mechanics, 46, pp.145-162, 1998 18.534 Mróz Z., IUTAM Symposium on Mechanics of Granular and Porous Materials, rozdział: Constitutive Modelling of Response of Granular Interface Layers, Springer Netherlands, series Solid Mechanics and its Applications, 53, pp.69-82, 1997 19.537 Mróz Z., Piekarski J., Advances in Structural Optimization, rozdział: First and Second Order Design Sensitivity at a Bifurcation Point, Springer Netherlands, series Solid Mechanics and Its Applications, 25, pp.349-380, 1995 20.535 Mróz Z., Stupkiewicz S., IUTAM Symposium on Microstructure-Property Interactions in Composite Materials, rozdział: Hysteretic Effects and Progressive Delamination at Composite Interfaces, Springer Netherlands, series Solid Mechanics and its Applications, 37, pp.247-264, 1995 21.533 Mróz Z., Rodzik P., Inelastic Behaviour of Structures under Variable Loads, rozdział: The Modified Multisurface Hardening Model and its Application to Cyclic Loading Problems, Springer Netherlands, series Solid Mechanics and Its Applications, 36, pp.3-18, 1995 22.532 Mróz Z., Optimization of Large Structural Systems, rozdział: Design sensitivity of critical loads and vibration frequencies of nonlinear structures, Springer Netherlands, NATO ASI Series E: Applied Sciences, 231, pp.455-476, 1993 23.543 Mróz Z., Dems K., Optimal Design with Advanced Materials, rozdział: Discrete and continuous reinforcement of materials and structures, Elsevier B.V., pp.383-405, 1993 24.528 Siemaszko A., Mróz Z., Progress in Structural Engineering, rozdział: Optimal Plastic Design of Imperfect Frame Structures, Springer Netherlands, series Solid Mechanics and Its Applications, 10, pp.353-370, 1991 25.54 Mróz Z., Haftka R.T., Buckling of Structures, rozdział: Sensitivity of Buckling Loads and Vibration Frequencies of Plates, Elsevier, series Studies in Applied Mechanics, 19, pp.255-266, 1988 26.53 Holnicki-Szulc J., Mróz Z., Structural Control, rozdział: Active Control of Stresses and Deflections of Elastic Structures by Means of Imposed Distortions, Springer Netherlands, pp.297-317, 1987 27.539 Mróz Z., The Optimum Shape, rozdział: Variational Approach to Shape Sensitivity Analysis and Optimal Design, Springer US, Part of the series General Motors Research Laboratories Symposia Series, pp.79-110, 1986 28.529 Pietruszczak S., Mróz Z., Mechanical Behavior of Anisotropic Solids / Comportment Méchanique des Solides Anisotropes, rozdział: Description of Anisotropic Consolidation of Clays, Springer Netherlands, pp.597-622, 1982
##### Redaktor monografii
 1.524 Mróz Z., Weichert D., Dorosz S., Inelastic Behaviour of Structures under Variable Loads, Kluwer Academic Publishers, series Solid Mechanics and its Applications, 36, pp.1-502, 1995