prof. dr hab. inż. Zenon Mróz 

Doktorat
1959  Nośność graniczna i kształtowanie wytrzymałościowe płyt i powłok
 20 
Habilitacja
Profesura
1971  Nadanie tytułu naukowego profesora 
Inne
1986  Członek korespondent Polskiej Akademii Nauk 
2004  Członek rzeczywisty Polskiej Akademii Nauk 
Promotor prac doktorskich
1.  20031027  Białas Marcin  Modelowanie rozwoju uszkodzeń w warstwach kontaktowych materiałów  
2.  19961219  Piekarski Jarosław  Wrażliwość i projektowanie optymalne nieliniowych układów sprężystych  
3.  19961128  Stupkiewicz Stanisław  Modelowanie poślizgów i rozwoju uszkodzeń w strefie kontaktu ciał sprężystoplastycznych  524  
4.  19961128  Maciejewski Jan  Analiza stanów pokrytycznych w procesach urabiania gruntów  
5.  19931216  Kowalczyk Maciej  Analiza stanów pokrytycznych w układach sprężystych i niesprężystych  
6.  19931216  Rodzik Piotr  Deformacja plastyczna metali przy zmiennych obciążeniach  
7.  19910103  Buczyński Andrzej (PW)  Stany graniczne w ośrodkach kruchoplastycznych  
8.  1989  Jarzębowski Andrzej  Modele konstytutywne dla materiałów rozdrobnionych i ich zastosowanie  
9.  19880712  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 lepkosprężystych  
14.  1980  Szeląg Daniel  Optymalizacja konstrukcji sprężystych przy zmiennych warunkach podparcia  
15.  1979  Pietruszczak Stanisław  Problemy brzegowe dla sprężystoplastycznych 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 sprężystoplastycznych materiałów rozdrobnionych o zmiennej gęstości  
19.  1974  Goss Czesław  Opis wzmocnienia plastycznego metali przy złożonych obciążeniach cyklicznych  
20.  1973  Grzymkowski Marian  Osiowosymetryczne 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 chemomechanical loading, COMPUTERS AND STRUCTURES, ISSN: 00457949, DOI: 10.1016/j.compstruc.2016.10.003, Vol.182, pp.7486, 2017 Streszczenie: The work presented here is focused on examining the size effect in concrete structures subjected to different loading conditions, which include a chemomechanical 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 alkalisilica reaction (ASR). In the latter case, a chemoplasticity framework is employed. The first set of simulations provides a deterministic assessment of the size effect in a series of threepoint 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’. Słowa kluczowe: Size effect, Alkalisilica reaction, 3D crack propagation, Embedded discontinuity model, Bifurcation analysis Afiliacje autorów:
 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: 01410296, DOI: 10.1016/j.engstruct.2017.03.011, Vol.141, pp.272291, 2017 Streszczenie: The paper presents a comprehensive experimental and numerical analysis of slender rectangular reinforced concrete beams with longitudinal BFRP bars without shear reinforcement subjected to 3point 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 elasticplasticdamage formulation. In order to describe strain localization in concrete, a nonlocal constitutive model was applied with account for a characteristic length of microstructure 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. Słowa kluczowe: BFRP bars, Concrete, Elasticplasticdamage, Nonlocal softening, Shear, Size effect, Strain localization Afiliacje autorów:
 35p.  
3.  Balevičius R.^{♦}, Mróz Z., Analytical Modelling of Combined Slip and Sliding Modes in Contact Interaction of Two Spherical Grains, Procedia Engineering, ISSN: 18777058, DOI: 10.1016/j.proeng.2017.02.020, Vol.172, pp.7582, 2017 Streszczenie: 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 slipsliding 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. Słowa kluczowe: soil, spherical grains contact interaction, slip and finite sliding modes, monotonic or reciprocal sliding, coefficients of friction and restitution Afiliacje autorów:
 
4.  Ziętek G.^{♦}, Mróz Z., A constitutive hardening model of coupled plastic deformation and martensitic transformation in steels, MECHANICS OF MATERIALS, ISSN: 01676636, DOI: 10.1016/j.mechmat.2016.06.004, Vol.100, pp.154166, 2016 Streszczenie: 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 tensioncompression and for combined tensiontorsion 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. Słowa kluczowe: Martensitic transformation, Plastic deformation, Back stresses, Yield and transformation conditions, Hardening rates Afiliacje autorów:
 40p.  
5.  Giusti S.M.^{♦}, Mróz Z., Novotny A.A.^{♦}, Sokołowski J.^{♦}, Topology design of thermomechanical actuators, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615147X, DOI: 10.1007/s0015801615930, pp.113, 2016 Streszczenie: 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 steadystate 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 elementbased examples for the topology design of thermomechanical actuators are presented. Słowa kluczowe: Shapetopology optimization, Topological derivative, Thermomechanical devices, Optimum design Afiliacje autorów:
 35p.  
6.  Páczelt I.^{♦}, Mróz Z., Analysis of Wear Processes for Periodic Loading, KEY ENGINEERING MATERIALS, ISSN: 16629795, DOI: 10.4028/www.scientific.net/KEM.681.117, Vol.681, pp.117141, 2016 Streszczenie: 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 inphase or outofphase 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. Słowa kluczowe: Contact Problems, Periodic Loading, Periodic SteadyStates, pVersion of Finite Elements, Sliding Wear Afiliacje autorów:
 
7.  SyrokaKorol E.^{♦}, Tejchman J.^{♦}, Mróz Z., FE investigations of the effect of fluctuating local tensile strength on coupled energeticstatistical size effect in concrete beams, ENGINEERING STRUCTURES, ISSN: 01410296, DOI: 10.1016/j.engstruct.2015.09.011, Vol.103, pp.239259, 2015 Streszczenie: 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 quasistatic three point bending within elastoplastic model assumptions, accounting for nonlocal 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. Słowa kluczowe: Autocorrelation length, Concrete beam, Elastoplasticity, Nonlocal softening, Random field, Size effect, Strain localization, Tensile strength Afiliacje autorów:
 35p.  
8.  Páczelt I.^{♦}, Mróz Z., Analysis of thermomechanical wear problems for reciprocal punch sliding, Advances in Engineering Software, ISSN: 09659978, DOI: 10.1016/j.advengsoft.2014.09.012, Vol.80, pp.139155, 2015 Streszczenie: 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. Słowa kluczowe: Contact optimization problems, Monotonic and periodic sliding wear, Heat generation, Steady wear state, Shape evolution, pversion of the finite element method Afiliacje autorów:
 30p.  
9.  Mróz Z., Mróz K.P., Analysis of delamination and damage growth in joined bilayer systems, Geomechanics for Energy and the Environment, ISSN: 23523808, DOI: 10.1016/j.gete.2015.10.001, Vol.4, No. Special Issue: 70th Anniversary of Professor Tomasz Hueckel, pp.428, 2015 Streszczenie: The analysis of mechanical response of joined bi or multilayer systems is a typical problem for both geomechanics and composite technology. The elastic or viscoelastic 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 bilayer 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 postcritical 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. Słowa kluczowe: Delamination, Cohesive zone, Shear lag, Damage process Afiliacje autorów:
 
10.  Páczelt I.^{♦}, Mróz Z., Baksa A.^{♦}, Analysis of steady wear processes for periodic sliding, Journal of Computational and Applied Mechanics, ISSN: 15862070, Vol.10, No.2, pp.231268, 2015 Streszczenie: 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. Słowa kluczowe: steady wear process, periodic sliding, unilateral contact, pversion of finite element method, shape optimization Afiliacje autorów:
 
11.  SyrokaKorol E.^{♦}, Tejchman J.^{♦}, Mróz Z., FE analysis of size effects in reinforced concrete beams without shear reinforcement based on stochastic elastoplasticity with nonlocal softening, FINITE ELEMENTS IN ANALYSIS AND DESIGN, ISSN: 0168874X, DOI: 10.1016/j.finel.2014.05.005, Vol.88, pp.2541, 2014 Streszczenie: 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 elastoplastic material exhibiting nonlocal 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. Słowa kluczowe: Elastoplasticity, Nonlocal softening, Random fields, Reinforced concrete beams, Size effect, Strain localization Afiliacje autorów:
 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: 00015970, DOI: 10.1007/s007070131016x, Vol.225, pp.17351759, 2014 Streszczenie: 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 loadcontrolled 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. Afiliacje autorów:
 25p.  
13.  Páczelt I.^{♦}, Mróz Z., On steady wear states for monotonic relative sliding of contacting bodies, KEY ENGINEERING MATERIALS, ISSN: 16629795, DOI: 10.4028/www.scientific.net/KEM.618.49, Vol.618, pp.4971, 2014 Streszczenie: The paper presents a synthetic review of recent research carried out by the writers [16, 79] 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 quasisteady 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 multizone contact problems for which both transient and steady states have been analyzed. Słowa kluczowe: Contact Optimization, PVersion of Finite Element Method, Steady Wear State, Variational Principles Afiliacje autorów:
 8p.  
14.  SyrokaKorol E.^{♦}, Tejchman J.^{♦}, Mróz Z., FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elastoplasticity and nonlocal softening, ENGINEERING STRUCTURES, ISSN: 01410296, DOI: 10.1016/j.engstruct.2012.09.013, Vol.48, pp.205219, 2013 Streszczenie: The numerical FE investigations of a deterministic and statistical size effect in unnotched concrete beams of similar geometry under quasistatic three point bending were performed within elastoplasticity with nonlocal 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. Słowa kluczowe: Concrete beam, Elastoplasticity, Latin hypercube sampling, Nonlocal softening, Stochastic fields, Size effect, Strain localization, Tensile strength Afiliacje autorów:
 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: 00015970, DOI: 10.1007/s0070701308399, Vol.224, No.8, pp.16591684, 2013 Streszczenie: 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. Afiliacje autorów:
 25p.  
16.  Mróz Z., Yanakieva A.^{♦}, Valeva V.^{♦}, Ivanova J.^{♦}, Analytical pullout analysis for carbon nanotubecement composites under static loading, Comptes rendus de l'Académie bulgare des Sciences, ISSN: 13101331, Vol.66, No.3, pp.431438, 2013 Streszczenie: The paper presents analytical pullout analysis for Carbon nanotubecement composite based on Shearlag 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) Constantτ model; (ii) Linear sliphardening model and, (iii) Linear slipsoftening 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. Słowa kluczowe: Carbon nanotube cement reinforced composites, Interface sliding models, Pullout analysis, Shearlag model, Static loading Afiliacje autorów:
 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: 22993649, Vol.20, No.2, pp.99112, 2013 Streszczenie: 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. Słowa kluczowe: thermomechanical analysis, high frequency cyclic loading, coating, design, FGM, optimization Afiliacje autorów:
 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: 18777058, DOI: 10.1016/j.proeng.2013.04.024, Vol.57, pp.167174, 2013 Streszczenie: 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. Słowa kluczowe: spheresphere 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 Afiliacje autorów:
 
19.  Páczelt I.^{♦}, Mróz Z., Solution of wear problems for monotonic and periodic sliding with pversion of finite element method, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2012.02.012, Vol.249252, pp.75103, 2012 Streszczenie: 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. Słowa kluczowe: Contact problems, Sliding wear, Steadystate, Periodic sliding, Optimal contact surface, pVersion of finite elements Afiliacje autorów:
 40p.  
20.  Páczelt I.^{♦}, Kucharski S., Mróz Z., The experimental and numerical analysis of quasisteady wear processes for a sliding spherical indenter, WEAR, ISSN: 00431648, DOI: 10.1016/j.wear.2011.08.026, Vol.274275, pp.127148, 2012 Streszczenie: 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 quasisteady 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 quasisteady 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. Słowa kluczowe: Spherical indenter, Sliding wear, Contact zone evolution, Wear parameters, Experimental data, Numerical simulation Afiliacje autorów:
 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: 1615147X, DOI: 10.1007/s0015801107103, Vol.45, pp.153169, 2012 Streszczenie: 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. Słowa kluczowe: Topological sensitivity, Elliptical hole, Plate, Plane crack, Optimal design Afiliacje autorów:
 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 ﬂatbottomed bin, PARTICUOLOGY, ISSN: 16742001, DOI: 10.1016/j.partic.2012.07.002, Vol.10, pp.672682, 2012 Streszczenie: The present paper provides both experimental and DEM analyses of the filling and discharge of pea grains from a 3D flatbottomed 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. Słowa kluczowe: Viscoelastic granular material, Discrete element method, Rolling friction, Wall pressure, Material velocity, Outflow mass, Outflow rate, Biosystems, Pea grains Afiliacje autorów:
 30p.  
23.  Kozicki J.^{♦}, Tejchman J.^{♦}, Mróz Z., Effect of grain roughness on strength, volume changes, elastic and dissipated energies during quasistatic homogeneous triaxial compression using DEM, GRANULAR MATTER, ISSN: 14345021, DOI: 10.1007/s1003501203521, Vol.14, pp.457468, 2012 Streszczenie: A quasistatic homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a threedimensional 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. Słowa kluczowe: Triaxial test, Granular material, Discrete element method, Grain roughness, Energy, Dissipation Afiliacje autorów:
 30p.  
24.  Dems K.^{♦}, Mróz Z., Analysis and design of thermomechanical interfaces, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 02397528, DOI: 10.2478/v1017501200274, Vol.60, No.2, pp.205213, 2012 Streszczenie: 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 firstorder 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. Słowa kluczowe: multiphase structures, sensitivity analysis, optimization, heat transfer, thermoelasticity Afiliacje autorów:
 30p.  
25.  Mróz Z., Bojczuk D.^{♦}, Shape and topology sensitivity analysis and its application to structural design, ARCHIVE OF APPLIED MECHANICS, ISSN: 09391533, DOI: 10.1007/s004190120672y, Vol.82, pp.15411555, 2012 Streszczenie: 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. Słowa kluczowe: Sensitivity analysis, Topological derivative, Structural design, Bar structures, Plates Afiliacje autorów:
 20p.  
26.  Kucharski S., Mróz Z., Identification of wear process parameters in reciprocating ballondisc tests, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2010.10.010, Vol.44, pp.154164, 2011 Streszczenie: 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. Słowa kluczowe: Dry wear, Contact area, Wear factor, Finite element method Afiliacje autorów:
 40p.  
27.  Páczelt I.^{♦}, Mróz Z., Numerical analysis of steady thermoelastic wear regimes induced by translating and rotating punches, COMPUTERS AND STRUCTURES, ISSN: 00457949, DOI: 10.1016/j.compstruc.2011.06.001, Vol.89, pp.24952521, 2011 Streszczenie: The present work provides the analysis of coupled thermoelastic 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 contactconformitycondition. 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. Słowa kluczowe: Contact problems, Sliding wear, Steady state, Thermal distortion, Optimal contact surface Afiliacje autorów:
 35p.  
28.  Balevičius R.^{♦}, Sielamowicz I.^{♦}, Mróz Z., Kačianauskas R.^{♦}, Investigation of wall stress and outflow rate in a flatbottomed bin: a comparison of the DEM model results with the experimental measurements, POWDER TECHNOLOGY, ISSN: 00325910, DOI: 10.1016/j.powtec.2011.08.042, Vol.214, pp.322336, 2011 Streszczenie: The present paper provides a discrete element method (DEM) analysis of the filling and discharge processes of granular material in a 3D flatbottomed 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. Słowa kluczowe: Viscoelastic granular material, Discrete element method, Wall pressure, Granular material stress, Microproperties, Bulk properties Afiliacje autorów:
 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: 09218831, DOI: 10.1016/j.apt.2010.12.005, Vol.22, pp.226235, 2011 Streszczenie: By using the discrete element method (DEM) a comparison and observations on material flow patterns in planewedged, spacewedged, and flatbottomed 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 interparticle friction. For validation of the performed simulations, velocity patterns developed in threedimensional flatbottomed 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. Słowa kluczowe: DEM, Mass flow rate, Velocity distribution, Planewedged, Spacewedged, Flatbottomed hoppers Afiliacje autorów:
 25p.  
30.  Mróz Z., Páczelt I.^{♦}, Analysis of thermoelastic wear problems, JOURNAL OF THERMAL STRESSES, ISSN: 01495739, DOI: 10.1080/01495739.2011.564026, Vol.34, pp.569606, 2011 Streszczenie: 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 quasisteady 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 steadystate is characterized by the minimum of wear dissipation power for which the stationary conditions generate the contact pressure distribution. The related steadystate 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. Słowa kluczowe: Contact optimization, Heat generation, Minimum principle,pversion of finite element method, Sliding wear, Steady wear state, Thermoelastic problem, Upwinding PetrovGalerkin scheme Afiliacje autorów:
 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.2134, 2011 Streszczenie: The elastoplastic 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 nonlinear 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 tensioncompression tests and for combined tensiontorsion tests. The cyclic stressstrain curves for specified strain amplitudes are used in material parameter calibration. Słowa kluczowe: plastic deformation, martensitic transformation, kinematic hardening, back stresses, cyclic deformation, increased hardening rates, decreased ratcheting strains Afiliacje autorów:
 
32.  Dems K.^{♦}, Mróz Z., Damage identification using modal, static and thermographic analysis with additional control parameters, COMPUTERS AND STRUCTURES, ISSN: 00457949, DOI: 10.1016/j.compstruc.2010.07.005, Vol.88, pp.12541264, 2010 Streszczenie: 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. Słowa kluczowe: Damage identification, Modal analysis, Static, dynamic and thermal loads, Assisting control parameters Afiliacje autorów:
 32p.  
33.  Mróz K.P., Mróz Z., On crack path evolution rules, ENGINEERING FRACTURE MECHANICS, ISSN: 00137944, DOI: 10.1016/j.engfracmech.2010.03.038, Vol.77, pp.17811807, 2010 Streszczenie: The models of crack growth in mixed mode conditions are reviewed for the plane and threedimensional (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 Tstress component. Monotonic and cyclic loading induced crack growth is considered. The energy and critical plane criteria based on local or nonlocal 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 MKcriterion 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. Słowa kluczowe: Fracture criteria, Tstress, Fatigue crack growth, 3D crack, Smooth and rough cracks, Crack path, Critical plane, Nonlocal models Afiliacje autorów:
 32p.  
34.  Páczelt I.^{♦}, Mróz Z., Variational approach to the analysis of steady state thermoelastic wear regimes, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.2709, Vol.81, pp.728760, 2010 Streszczenie: A transient wear process on frictional interface of two thermoelastic 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 steadystate contact shapes by accounting for coupled wear and thermal distortion effects. Afiliacje autorów:
 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: 1615147X, DOI: 10.1007/s0015800803335, Vol.39, pp.115, 2009 Streszczenie: 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. Słowa kluczowe: Topological sensitivity derivative, Finite topology modifications, Bending plates, Optimal topology and shape, Optimal layout of ribs Afiliacje autorów:
 32p.  
36.  Páczelt I.^{♦}, Mróz Z., On the analysis of steadystate sliding wear processes, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2008.06.007, Vol.42, No.2, pp.275283, 2009 Streszczenie: 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 weardissipation 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 nonlinear 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 runin periods. The extension to cyclic translation cases can be generated by considering steady cyclic states of wear processes. Słowa kluczowe: Contact problems, Sliding wear, Steadystate, Variational principle, Optimal contact surface Afiliacje autorów:
 32p.  
37.  Mróz Z., Janusz Klepaczko remembered, INTERNATIONAL JOURNAL OF IMPACT ENGINEERING, ISSN: 0734743X, DOI: 10.1016/j.ijimpeng.2009.02.003, Vol.36, No.8, pp.994994, 2009  
38.  Balevičius R.^{♦}, Kačianauskas R.^{♦}, Mróz Z., Sielamowicz I.^{♦}, Discrete particle investigation of friction effect in filling and unsteady/steady discharge in threedimensional wedge shaped hopper, POWDER TECHNOLOGY, ISSN: 00325910, DOI: 10.1016/j.powtec.2008.02.006, Vol.187, No.2, pp.159174, 2008 Streszczenie: The friction effect in filling and unsteady/steady discharge of threedimensional wedgeshaped 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 interparticle friction coefficient over the range of 0–0.6. A comparison of the numerical results with available continuumbased predictions was also presented. Słowa kluczowe: Viscoelastic granular material, 3D wedgeshaped hopper, Discrete element method, Wall pressure, Granular stresses, Fraction discharged, Bulk porosity Afiliacje autorów:
 
39.  Maciejewski J., Mróz Z., An upperbound analysis of axisymmetric extrusion assisted by cyclic torsion, JOURNAL OF MATERIALS PROCESSING TECHNOLOGY, ISSN: 09240136, DOI: 10.1016/j.jmatprotec.2007.12.061, Vol.206, pp.333344, 2008 Streszczenie: 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 rigidperfectly plastic and the upperbound 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. Słowa kluczowe: Extrusion, Cyclic torsion, KOBO method, Upperbound analysis, Process control parameters Afiliacje autorów:
 
40.  Raniecki B., Mróz Z., Yield or martensitic phase transformation conditions and dissipation functions for isotropic, pressureinsensitive alloys exhibiting SD effect, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/s0070700705447, Vol.195, pp.81102, 2008 Streszczenie: 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. Afiliacje autorów:
 
41.  Wilczyński B.^{♦}, Mróz Z., Optimal design of machine components using notch correction and plasticity models, COMPUTERS AND STRUCTURES, ISSN: 00457949, DOI: 10.1016/j.compstruc.2006.08.092, Vol.85, pp.13821398, 2007 Streszczenie: 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. Słowa kluczowe: Low cycle fatigue, Notch correction, Plasticity models, Fatigue life prediction, Life time maximization, Shape optimization Afiliacje autorów:
 
42.  Kucharski S., Mróz Z., Identification of yield stress and plastic hardening parameters from a spherical indentation test, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 00207403, DOI: 10.1016/j.ijmecsci.2007.03.013, Vol.49, No.11, pp.12381250, 2007 Streszczenie: 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. Słowa kluczowe: Spherical indentation test, Identification, Finite element modelling, Elastoplastic material properties Afiliacje autorów:
 
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: 00207683, DOI: 10.1016/j.ijsolstr.2006.05.027, Vol.44, No.34, pp.895925, 2007 Streszczenie: 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. Słowa kluczowe: Sliding wear, Contact optimization, Steady wear state, pVersion of finite element method Afiliacje autorów:
 
44.  Białas M., Mróz Z., An energy model of segmentation cracking of thin films, MECHANICS OF MATERIALS, ISSN: 01676636, DOI: 10.1016/j.mechmat.2007.02.004, Vol.39, No.9, pp.845864, 2007 Streszczenie: 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. Słowa kluczowe: Segmentation cracking, Delamination, Fracture energy, Oxide coating Afiliacje autorów:
 
45.  Balevičius R.^{♦}, Kačianauskas R.^{♦}, Mróz Z., Sielamowicz I.^{♦}, Microscopic and macroscopic analysis of granular material behaviour in 3D flatbottomed hopper by the discrete element methody, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.59, pp.231257, 2007 Streszczenie: The paper presents the application of the discrete element method to modelling of granular material filling and discharge in 3D flatbottomed hopper. A mathematical model, as well as the developed software code, operates with spherical viscoelastic noncohesive 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 interparticle 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 macrophenomena in the timedependent flow process. Słowa kluczowe: discrete element method, spherical particles, viscoelastic granular material, threedimensional flat bottomed hopper Afiliacje autorów:
 
46.  Mróz Z., Ziętek G.^{♦}, Modeling of cyclic hardening of metals coupled with martensitic transformation, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.59, No.1, pp.320, 2007 Streszczenie: The work presents an elastoplastic 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. Afiliacje autorów:
 
47.  KowalczykGajewska K., Mróz Z., Pęcherski R.B., Micromechanical modelling of polycrystalline materials under nonproportional deformation paths, ARCHIVES OF METALLURGY AND MATERIALS, ISSN: 17333490, Vol.52, pp.181192, 2007 Streszczenie: The rigidplastic crystal plasticity model with single yield surface of 2ndegree is applied to simulate the polycrystalline behaviour and the crystallographic texture development under nonproportional deformation paths. The role of two controlling parameters: the amplitude and frequency for the processes of tension or compression assisted by cyclic torsion of thinwalled tubes made of copper is analysed. The effect of microshear 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. Słowa kluczowe: micromechanics, modelling of materials, rigidplastic solids, crystal plasticity, texture, cyclic torsion, nonproportional deformation path, microshear bands Afiliacje autorów:
 
48.  Maciejewski J., Mróz Z., Analiza procesu wyciskania metali wspieranego deformacją cykliczną, RUDY I METALE NIEŻELAZNE, ISSN: 00359696, Vol.11, pp.668677, 2007 Streszczenie: Przedstawiono analizę procesu osiowosymetrycznego wyciskania metali przy nałożeniu cyklicznego skręcania wywoływanego matrycą ( metoda KOBO, [1÷4]). Założono uproszczony model sztywnoplastycznego materiału bez wzmocnienia i kinematycznie dopuszczalny mechanizm płynięcia. Z warunku równości mocy dyssypacji plastycznej i mocy sił zewnętrznych (siła osiowa i moment skręcający) określono wartość [...] Afiliacje autorów:
 
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: 01787675, DOI: 10.1007/s0046600506745, Vol.37, pp.349361, 2006 Streszczenie: In this paper, the motion of a deformable body sliding on a halfplane 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 slidingdirection 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. Słowa kluczowe: Elliptic friction criterion, Large sliding, Variational formulation, Uzawa algorithm Afiliacje autorów:
 
50.  Białas M., Mróz Z., Crack patterns in thin layers under temperature loading. Part I. Monotonic loading, ENGINEERING FRACTURE MECHANICS, ISSN: 00137944, DOI: 10.1016/j.engfracmech.2005.10.012, Vol.73, pp.917938, 2006 Streszczenie: 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. Słowa kluczowe: Cohesive zone modelling, Segmentation cracking, Delamination, Temperature loading Afiliacje autorów:
 
51.  Białas M., Mróz Z., Crack patterns in thin layers under temperature loading. Part II. Cyclic loading, ENGINEERING FRACTURE MECHANICS, ISSN: 00137944, DOI: 10.1016/j.engfracmech.2005.10.013, Vol.73, pp.939952, 2006 Streszczenie: 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. Słowa kluczowe: Cohesive zone modelling, Segmentation cracking, Delamination, Cyclic loading, Temperature loading Afiliacje autorów:
 
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 NONLINEAR MECHANICS, ISSN: 00207462, DOI: 10.1016/j.ijnonlinmec.2006.08.002, Vol.41, No.8, pp.936948, 2006 Streszczenie: This paper presents numerical investigations on the loading and unloading of a threedimensional 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. Słowa kluczowe: Elliptic friction criterion, nonassociated slip rile, Uzawa algorithm, Cyclic loading Afiliacje autorów:
 
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: 1615147X, DOI: 10.1007/s001580050596z, Vol.31, pp.163175, 2006 Streszczenie: Multiobjective approach for optimization of the discharge flow parameters of viscoelastic frictional granular material in a wedgeshaped 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. Słowa kluczowe: Viscoelastic granular material, Hopper, Discrete element method, Optimization of flow parameters Afiliacje autorów:
 
54.  Mróz Z., KowalczykGajewska K., Maciejewski J., Pęcherski R.B., Tensile or compressive plastic deformation of cylinders assisted by cyclic torsion, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.58, No.6, pp.497527, 2006 Streszczenie: 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 rigidperfectly plastic or elasticperfectly 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 Słowa kluczowe: cyclic torsion, plastic deformation of cylinders, elasticperfectly plastic model, rigidperfectly plastic model, analytical solutions of cyclic response of a cylinder Afiliacje autorów:
 
55.  Dems K.^{♦}, Mróz Z., Application of thermographic fields in identification of structural properties and defects, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 22993649, Vol.13, No.1, pp.319, 2006 Streszczenie: 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, quasistatically 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 gradientoriented methods are used. The proper sensitivities of introduced identification functional are also derived. Some simple examples illustrate the applicability of the proposed approach. Słowa kluczowe: identification, sensitivity, thermographic methods, pathindependent integrals Afiliacje autorów:
 
56.  Mróz Z., Bojczuk D.^{♦}, Topological sensitivity derivative: application in optimal design and material science, FOUNDATIONS OF CIVIL AND ENVIRONMENTAL ENGINEERING, ISSN: 16429303, Vol.7, pp.229250, 2006 Streszczenie: 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. Słowa kluczowe: topological derivative, finite topology variation, structure and material evolution, optimal topology and shape Afiliacje autorów:
 
57.  Páczelt I.^{♦}, Mróz Z., On optimal contact shapes generated by wear, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.1321, Vol.63, pp.12501287, 2005 Streszczenie: 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. Afiliacje autorów:
 
58.  Białas M., Mróz Z., Modelling of progressive interface failure under combined normal compression and shear stress, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/j.ijsolstr.2005.01.006, Vol.42, No.15, pp.44364467, 2005 Streszczenie: 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 antiplane 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 quasistatic progressive delamination process clarifies the character of critical points and postcritical 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. Słowa kluczowe: Interface, Debonding, Cohesive zone, Instability points Afiliacje autorów:
 
59.  Mróz Z., Garstecki A.^{♦}, Optimal loading conditions in the design and identification of structures. Part I: Discrete formulation, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615147X, DOI: 10.1007/s0015800404740, Vol.29, No.1, pp.118, 2005 Streszczenie: 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. Słowa kluczowe: optimization, sensitivity analysis, structural identification, variable loading conditions Afiliacje autorów:
 
60.  Bojczuk D.^{♦}, Mróz Z., Determination of optimal actuator forces and positions in smart structures using adjoint method, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615147X, DOI: 10.1007/s0015800505171, Vol.30, No.4, pp.308319, 2005 Streszczenie: 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. Słowa kluczowe: Smart structures, Actuators, Adjoint method, Optimal active support Afiliacje autorów:
 
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: 8756758X, DOI: 10.1111/j.14602695.2004.00829.x, Vol.28, pp.6171, 2005 Streszczenie: The present paper is concerned with modelling of fatigue crack initiation and propagation by applying the nonlocal 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. Afiliacje autorów:
 
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: 03639061, DOI: 10.1002/nag.417, Vol.29, No.4, pp.337368, 2005 Streszczenie: 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 antiplane 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. Afiliacje autorów:
 
63.  Kačianauskas R.^{♦}, Mróz Z., Żarnovskij V.^{♦}, Stupak E.^{♦}, Threedimensional correction of the stress intensity factor for plate with a notch, INTERNATIONAL JOURNAL OF FRACTURE, ISSN: 03769429, DOI: 10.1007/s1070400544011, Vol.136, pp.7598, 2005 Streszczenie: The 3D effects of the 2D mode I stress intensity factor for the plate with a Vshaped straight throughthickness notch are investigated by the finite element method and threedimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (outofplane degree of freedom). The 3D finite element mesh generator combining the 2D inplane adaptive unstructured mesh with the structured throughthickness mesh Is developed and applied for the analysis purposes. Threedimensionality was examined by using two independent indicators, namely, stress or strainbased constraint factors. The threepoint bend and tensile centercracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for threepoint bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile centercracked 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. Słowa kluczowe: Constraint factor, finite element method, plate with a notch, threedimensional stress intensity factor Afiliacje autorów:
 
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 ASTRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 09215093, DOI: 10.1016/j.msea.2005.08.208, Vol.412, pp.241251, 2005 Streszczenie: 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 chargecoupled 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 asreceived 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 beamphysical vapour deposition (EBPVD) 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 beamphysical vapour deposition coatings. Słowa kluczowe: Cohesive zone modelling, Segmentation cracking, Thin film coating, Bending test Afiliacje autorów:
 
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: 14292955, Vol.34, pp.1530, 2005  
66.  Hjiaj M.^{♦}, Feng Z.Q.^{♦}, de Saxcé G.^{♦}, Mróz Z., Threedimensional finite element computations for frictional contact problems with nonassociated sliding rule, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.1037, Vol.60, No.12, pp.20452076, 2004 Streszczenie: This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is nonassociated.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 nonassociated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semiaxes ratio. The frictional contact law and its inverse are derived from a single nondifferentiable scalarvalued function, called a bipotential. The convexity properties of the bipotential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the timeintegration 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, nocontact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour. Afiliacje autorów:
 
67.  Kucharski S., Mróz Z., Identification of material parameters by means of compliance moduli in spherical indentation test, MATERIALS SCIENCE AND ENGINEERING ASTRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 09215093, DOI: 10.1016/j.msea.2004.03.030, Vol.379, No.12, pp.448456, 2004 Streszczenie: 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 Fullsize 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. Słowa kluczowe: Spherical indentation test, Identification, Elastoplastic material properties, Indentation compliance moduli Afiliacje autorów:
 
68.  Seweryn A.^{♦}, Tomczyk A.^{♦}, Mróz Z., A nonlocal fatigue crack growth model and its experimental verification, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 14292955, Vol.42, No.1, pp.6982, 2004 Streszczenie: The present paper is concerned with the modelling of fatigue crack initiation and propagation by applying the nonlocal 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 tensioncompression conditions. The predictions are compared with experimental data. Słowa kluczowe: fatigue, damage accumulation, crack propagation Afiliacje autorów:
 
69.  Boukpeti N.^{♦}, Mróz Z., Drescher A.^{♦}, Modeling rate effects in undrained loading of sands, Canadian Geotechnical Journal, ISSN: 00083674, DOI: 10.1139/t03077, Vol.41, No.2, pp.342350, 2004 Streszczenie: 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 timedependent 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, elasticviscoplastic behavior. Afiliacje autorów:
 
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: 00207225, DOI: 10.1016/j.ijengsci.2003.10.004, Vol.42, No.10, pp.10131034, 2004 Streszczenie: In this paper, the formulation of complex anisotropic frictional models with orthotropic friction condition and nonassociated 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 semiaxis ratio, which lead to a nonassociated 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 bipotential. Due to the nonassociated 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 bifunctional, that depends on both the displacements and the stresses. Słowa kluczowe: Superelliptic friction criterion, Nonassociated sliding rule, Bipotential, Variational formulation Afiliacje autorów:
 
71.  Mróz Z., Bojczuk D.^{♦}, Finite topology variations in optimal design of structures, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615147X, DOI: 10.1007/s0015800302894, Vol.25, No.3, pp.153173, 2003 Streszczenie: 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. Słowa kluczowe: optimal topology, finite topology modifications, structure evolution, truss and frame structures Afiliacje autorów:
 
72.  Kowalczyk K., Mróz Z., Description of anisotropy of textured metals using macro and micro models, JOURNAL DE PHYSIQUE IV, ISSN: 11554339, DOI: 10.1051/jp4:20030188, Vol.105, pp.199206, 2003 Streszczenie: In the paper description of anisotropy of textured metals using macro and micro models is compared. In the present macroapproach 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 microapproach and could prove convenient in the analysis of technological processes for textured materials. Afiliacje autorów:
 
73.  Mróz Z., Sielamowicz I.^{♦}, Deformation Zones in Granular Materials in Hoppers During Filling and Emptying Processes, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867888X, Vol.51, No.4, pp.461491, 2003 Streszczenie: 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 stressstrain relations are satisfied for cylindrical slice elements assuming dependence of displacement and stress on radial coordinate. The elastic or elastoplastic material model is used with the Coulomb yield condition and nonassociated 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. Afiliacje autorów:
 
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: 07496419, DOI: 10.1016/S07496419(01)000377, Vol.19, No.3, pp.323344, 2003 Streszczenie: 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 micromechanical models and with experimental data. Słowa kluczowe: Cutting and forming, Constitutive behaviour, Ideally plastic material, Frictional contact Afiliacje autorów:
 
75.  Mróz Z., Boukpeti N.^{♦}, Drescher A.^{♦}, Constitutive model for static liquefaction, International Journal of Geomechanics, ISSN: 15323641, DOI: 10.1061/(ASCE)15323641(2003)3:2(133)#sthash.LLxWvMhd.dpuf, Vol.3, No.2, pp.133144, 2003 Streszczenie: A general, threedimensional 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 planestrain compression is presented and compared with the response in triaxial compression/extension loading. Static and kinematic instability states also are discussed. Afiliacje autorów:
 
76.  Hjiaj M.^{♦}, de Saxcé G.^{♦}, Mróz Z., A variational inequalitybased formulation of the frictional contact law with a nonassociated sliding rule, EUROPEAN JOURNAL OF MECHANICS ASOLIDS, ISSN: 09977538, DOI: 10.1016/S09977538(01)011834, Vol.21, No.1, pp.4959, 2002 Streszczenie: We present a variational formulation of a complex frictional contact law with anisotropic friction condition and a nonassociated sliding rule. The distinguishing characteristic of the proposed formulation is that the interface law, as well as its inverse, derive from a single scalarvalued function called bipotential. This function, which depends on both the velocities and the associated forces, is split into the sum of two dual pseudopotentials 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 bipotential that can be exploited for numerical purposes. Afiliacje autorów:
 
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: 03639061, DOI: 10.1002/nag.207, Vol.26, No.4, pp.407431, 2002 Streszczenie: 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 nonlinear 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. Afiliacje autorów:
 
78.  Mróz Z., Oliferuk W., Energy balance and identification of hardening moduli in plastic deformation processes, International Journal of Plasticity, ISSN: 07496419, DOI: 10.1016/S07496419(00)001030, Vol.18, No.3, pp.379397, 2002 Streszczenie: 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, austeniticferritic steel and Fe–Si alloy. Słowa kluczowe: Thermomechanical processes, Hardening modulus, Polycrystalline material, Energy methods, Mechanical testing Afiliacje autorów:
 
79.  Boukpeti N.^{♦}, Mróz Z., Drescher A.^{♦}, A model for static liquefaction in triaxial compression and extension, Canadian Geotechnical Journal, ISSN: 00083674, DOI: 10.1139/t02066, Vol.39, No.6, pp.12431253, 2002 Streszczenie: 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 nonassociated flow rule is used. The isotropic hardeningsoftening 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 phasetransformation states also are discussed, and the energy of liquefaction is quantified.Key words: static liquefaction, constitutive model, triaxial tests, liquefaction energy. Afiliacje autorów:
 
80.  Valeva V., Ivanova J.^{♦}, Mróz Z., Parametric analysis of the decay rate of end effects in heat conduction for multilayered semiinfinite sandwich structures, Journal of Theoretical and Applied Mechanics, BULGARIAN ACADEMY OF SCIENCES, ISSN: 13139665, Vol.32, No.4, pp.3952, 2002 Streszczenie: This article is concerned with the effect of imperfect interfaces on the decay of end effect for heat conduction in nonsymmetric sandwich strip with  layers. The constituent layers are isotropic and the interface conditions between the layers are assumed to be either LCtype or HCtype at vanishing temperature at the bottom and top side of the strip. The characteristic decay length in all considered cases for threelayered 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 threelayered 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. Słowa kluczowe: decay rate of end effects, heat condition, semiinfinite sandwich structure Afiliacje autorów:
 
81.  Mróz Z., On unjustified criticism of Green's formula for Hencky plates with microperiodic structure, Nonlinear Analysis: Theory, Methods & Applications, ISSN: 0362546X, DOI: 10.1016/S0362546X(01)001006, Vol.49, No.2, pp.293, 2002  
82.  Pietruszczak S., Mróz Z., On failure criteria for anisotropic cohesivefrictional materials, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 03639061, DOI: 10.1002/nag.141, Vol.25, No.5, pp.509524, 2001 Streszczenie: 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. Afiliacje autorów:
 
83.  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: 03639061, DOI: 10.1002/nag.160, Vol.25, No.9, pp.909932, 2001 Streszczenie: 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. Afiliacje autorów:
 
84.  Kucharski S., Mróz Z., Identification of plastic hardening parameters of metals from spherical indentation tests, MATERIALS SCIENCE AND ENGINEERING ASTRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 09215093, DOI: 10.1016/S09215093(01)01334X, Vol.318, No.12, pp.6576, 2001 Streszczenie: Using the twoparameter 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 lowalloy steel are used to assess the accuracy of the identification procedure. Finally, identification of the stress–strain curve of an aluminium alloy is demonstrated. Słowa kluczowe: Spherical indentation tests, Plastic, Lowalloy steel, Metals Afiliacje autorów:
 
85.  Giambanco G.^{♦}, Mróz Z., The Interphase Model for the Analysis of Joints in Rock Masses and Masonry Structures, MECCANICA, ISSN: 00256455, DOI: 10.1023/A:1011957217840, Vol.36, No.1, pp.111130, 2001 Streszczenie: 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. Słowa kluczowe: Softening, Contact, Interfaces, Cohesive joint Afiliacje autorów:
 
86.  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: 14292955, Vol.39, No.3, pp.707739, 2001 Streszczenie: 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 micromechanical 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. Afiliacje autorów:
 
87.  Xinpu S.^{♦}, Mróz Z., Bingye X.^{♦}, Constitutive theory of plasticity coupled with orthotropic damage for geomaterials, APPLIED MATHEMATICS AND MECHANICSENGLISH EDITION, ISSN: 02534827, DOI: 10.1007/BF02438321, Vol.22, No.9, pp.10281034, 2001 Streszczenie: 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 MohrCoulomb 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 socalled damage strain. Słowa kluczowe: damage plasticity, coupling, dilatancy, geomaterial Afiliacje autorów:
 
88.  Sergeyev O.^{♦}, Mróz Z., Sensitivity analysis and optimal design of 3D frame structures for stress and frequency constraints, COMPUTERS AND STRUCTURES, ISSN: 00457949, DOI: 10.1016/S00457949(99)000887, Vol.75, No.2, pp.167185, 2000 Streszczenie: The present paper deals with the problem of determining the optimal joint positions and crosssectional 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 selfweight 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. Afiliacje autorów:
 
89.  Pietruszczak S.^{♦}, Mróz Z., Formulation of anisotropic failure criteria incorporating a microstructure tensor, COMPUTERS AND GEOTECHNICS, ISSN: 0266352X, DOI: 10.1016/S0266352X(99)000348, Vol.26, No.2, pp.105112, 2000 Streszczenie: 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. Afiliacje autorów:
 
90.  Mróz Z., On the stability of friction contact, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 14292955, Vol.38, No.2, pp.315329, 2000 Streszczenie: 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 rigidsliding and elasticsliding contacts obeying the Coulomb friction condition and the nonassociated sliding rule. Both static and dynamic modes are considered. Słowa kluczowe: contact friction, stability, static and dynamic modes Afiliacje autorów:
 
91.  Xinpu S.^{♦}, Mróz Z., Shear beam model for interface failure under antiplane shear (I)Fundamental behavior, APPLIED MATHEMATICS AND MECHANICSENGLISH EDITION, ISSN: 02534827, DOI: 10.1007/BF02459242, Vol.21, No.11, pp.12211228, 2000 Streszczenie: 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. Słowa kluczowe: interface layer, cohesive layer, antiplane shear, shear beam model, failure, instability, damage Afiliacje autorów:
 
92.  Xinpu S.^{♦}, Mróz Z., Shear beam model for interface failure under antiplane shear (II)— Instability, APPLIED MATHEMATICS AND MECHANICSENGLISH EDITION, ISSN: 02534827, DOI: 10.1007/BF02459243, Vol.21, No.11, pp.12291236, 2000 Streszczenie: 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, snapback or snapthrough, was established;2) analytical solution was given out for the double shear beam and the loaddisplacement diagram for monotonic loading was presented for a full process; and3) the problem of the energy release induced by instability was discussed. Słowa kluczowe: interface layer, antiplane shear, failure, shear beam model, instability, snapthrough, snapback, damage Afiliacje autorów:
 
93.  Stupkiewicz S., Mróz Z., A model of third body abrasive friction and wear in hot metal forming, WEAR, ISSN: 00431648, DOI: 10.1016/S00431648(99)001246, Vol.231, No.1, pp.124138, 1999 Streszczenie: A model of friction accounting for third body particles at the contact interface is derived from a simple micromechanical 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. Słowa kluczowe: Contact friction, Wear, Hot metal forming, Third body abrasion Afiliacje autorów:
 
94.  Nawrocki P., Mróz Z., A constitutive model for rock accounting for viscosity and yield stress degradation, COMPUTERS AND GEOTECHNICS, ISSN: 0266352X, DOI: 10.1016/S0266352X(99)000208, Vol.25, No.4, pp.247280, 1999 Streszczenie: 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 postcritical stages. Afiliacje autorów:
 
95.  Bojczuk D.^{♦}, Mróz Z., Optimal topology and configuration design of trusses with stress and buckling constraints, Structural optimization, ISSN: 09344373, DOI: 10.1007/BF01197710, Vol.17, No.1, pp.2535, 1999 Streszczenie: A heuristic algorithm for optimal design of trusses is presented with account for stress and buckling constraints. The design variables are constituted by crosssectional 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 firstorder sensitivity derivatives provide the necessary information on topology variation and the optimality conditions for configuration and crosssectional parameters. Afiliacje autorów:
 
96.  Mróz Z., Piekarski J., Sensitivity analysis and optimal design of nonlinear structures, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/(SICI)10970207(19980815)42:7<1231::AIDNME407>3.0.C, Vol.42, No.7, pp.12311262, 1998 Streszczenie: Sensitivity analysis for nonlinear 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 postcritical 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. Afiliacje autorów:
 
97.  Mróz Z., Stupkiewicz S., Constitutive model of adhesive and ploughing friction in metalforming processes, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 00207403, DOI: 10.1016/S00207403(97)000556, Vol.40, No.23, pp.281303, 1998 Streszczenie: In metalforming processes the toolworkpiece 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 nonassociated slip rule. The model parameters can be identified from micromechanical 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. Słowa kluczowe: contact friction, metal forming, asperity flattening, ploughing Afiliacje autorów:
 
98.  Seweryn A.^{♦}, Mróz Z., On the criterion of damage evolution for variable multiaxial stress states, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/S00207683(97)001212, Vol.35, No.14, pp.15891616, 1998 Streszczenie: 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 nonlocal 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 fourthorder damage tensors in order to describe damage distribution within the element, and the associated compliance variation are introduced. Afiliacje autorów:
 
99.  Nawrocki P., Mróz Z., A viscoplastic degradation model for rocks, INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES, ISSN: 13651609, DOI: 10.1016/S01489062(98)000126, Vol.35, No.7, pp.9911000, 1998 Streszczenie: 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 prepeak hardening and postpeak softening response of rock material in compression providing good simulation of material response in both stable and postcritical 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. Afiliacje autorów:
 
100.  Dems K.^{♦}, Mróz Z., Sensitivity analysis and optimal design of external boundaries and interfaces for heat conduction systems, JOURNAL OF THERMAL STRESSES, ISSN: 01495739, Vol.21, No.34, pp.461488, 1998 Streszczenie: A heat conduction problem within a thermal anisotropic solid body is formulated. With respect to an arbitrary thermal functional defined over space domain, its firstorder 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. Afiliacje autorów:
 
101.  Bojczuk D.^{♦}, Mróz Z., Optimal Design of Trusses with Account for Topology Variation, Mechanics of Structures and Machines, ISSN: 15397734, DOI: 10.1080/08905459808945418, Vol.26, No.1, pp.2140, 1998 Streszczenie: In this paper, a heuristic algorithm is presented for optimal design of trusses with varying crosssectional 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. Afiliacje autorów:
 
102.  Seweryn A.^{♦}, Poskrobko S.^{♦}, Mróz Z., Brittle Fracture in Plane Elements with Sharp Notches under MixedMode Loading, JOURNAL OF ENGINEERING MECHANICSASCE, ISSN: 07339399, DOI: 10.1061/(ASCE)07339399(1997)123:6(535), Vol.123, No.6, pp.535543, 1997 Streszczenie: Plane structural elements with sharp wedgeshaped notches are considered and the conditions for crack initiation are discussed. The use of the Griffith energy condition would require the assumption of preexistence 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. Mixedmode 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 mixedmode 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)07339399(1997)123%3A6(535)#sthash.M6SKEj2w.dpuf Afiliacje autorów:
 
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: 03639061, DOI: 10.1002/(SICI)10969853(199601)20:1<1::AIDNAG799>3.0.CO;2L, Vol.20, No.1, pp.133, 1996 Streszczenie: 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 nonsymmetric 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. Afiliacje autorów:
 
104.  Mróz Z., Bojczuk D.^{♦}, Sensitivity Analysis of Truss and Frame Structures in Critical States, Mechanics of Structures and Machines, ISSN: 15397734, DOI: 10.1080/08905459608905258, Vol.24, No.1, pp.105134, 1996 Streszczenie: 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 crosssectional and configuration parameters. The effect of redistribution during the prebuckling state is considered. Afiliacje autorów:
 
105.  Seweryn A.^{♦}, Mróz Z., A nonlocal stress failure condition for structural elements under multiaxial loading, ENGINEERING FRACTURE MECHANICS, ISSN: 00137944, DOI: 10.1016/00137944(94)00335F, Vol.51, No.6, pp.955973, 1995 Streszczenie: A nonlocal stress condition for crack initiation and propagation is proposed and applied to several particular cases, such as plate with wedgeshaped 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 nonlocal condition, which is applicable to both regular and singular stress concentrations. Afiliacje autorów:
 
106.  Dems K.^{♦}, Mróz Z., Shape sensitivity in mixed DirichletNeumann boundaryvalue problems and associated class of pathindependent integrals, EUROPEAN JOURNAL OF MECHANICS ASOLIDS, ISSN: 09977538, Vol.14, No.2, pp.169203, 1995 Streszczenie: Considering an arbitrary behavioural functional specified for a mixed DirichletNeumann boundaryvalue 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 pathindependent 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 integrals Słowa kluczowe: Numerical method, Boundaryvalue problems, Path integral, Sensitivity analysis, Holes, Optimization, Geometrical shape Afiliacje autorów:
 
107.  Mróz Z., Rodzik P., On the control of deformation process by plastic strain, International Journal of Plasticity, ISSN: 07496419, DOI: 10.1016/S07496419(95)000313, Vol.11, No.7, pp.827842, 1995 Streszczenie: 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 postcritical states occur for stress or strain control. Afiliacje autorów:
 
108.  Mróz Z., Stupkiewicz S., An anisotropic friction and wear model, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(94)901678, Vol.31, No.8, pp.11131131, 1994 Streszczenie: 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. Afiliacje autorów:
 
109.  Mróz Z., Design sensitivity analysis of nonlinear structures in regular and critical states, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(94)901910, Vol.31, No.15, pp.20712098, 1994 Streszczenie: A general design sensitivity formulation is introduced for nonlinear 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 postcritical 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 postbuckling fields in the case of symmetric bifurcation. Afiliacje autorów:
 
110.  Stupkiewicz S., Mróz Z., Elastic beam on a rigid frictional foundation under monotonic and cyclic loading, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(94)900248, Vol.31, No.24, pp.34193442, 1994 Streszczenie: 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 selfsimilarity 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. Afiliacje autorów:
 
111.  Mróz Z., Jarzębowski A., Phenomenological model of contact slip, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01178518, Vol.102, No.1, pp.5972, 1994 Streszczenie: 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. Afiliacje autorów:
 
112.  Jarzębowski A., Mróz Z., On slip and memory rules in elastic, friction contact problems, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01178527, Vol.102, No.1, pp.199216, 1994 Streszczenie: 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 nonproportional loading cases. Afiliacje autorów:
 
113.  Bojczuk D.^{♦}, Mróz Z., Sensitivity analysis for nonlinear beams and frames, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 14292955, Vol.32, No.4, pp.867886, 1994 Streszczenie: A geometrically nonlinear, elastic frame structure is considered and the effect of small variation of its parameters on structure deformation response is studied. Variations of crosssectional 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. Afiliacje autorów:
 
114.  Li Z.X.^{♦}, Mróz Z., Damage model for viscoplasticsoftening behavior: cement paste and concrete, Theoretical and Applied Fracture Mechanics, ISSN: 01678442, DOI: 10.1016/01678442(94)000050, Vol.20, No.2, pp.105113, 1994 Streszczenie: A viscoplasticsoftening model is developed; it invokes damage accumulation depending on the viscous strain and stress rates. For deformation beyond the peak on the uniaxial stressstrain 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. Afiliacje autorów:
 
115.  Dems K.^{♦}, Mróz Z., On shape sensitivity approaches in the numerical analysis of structures, Structural optimization, ISSN: 09344373, DOI: 10.1007/BF01743340, Vol.6, No.2, pp.8693, 1993 Streszczenie: The semianalytical, analytical and direct methods for numerical structural shape sensitivity analysis are discussed for a beam model and the general threedimensional 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. Afiliacje autorów:
 
116.  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: 00207683, DOI: 10.1016/00207683(92)90209C, Vol.29, No.4, pp.437463, 1992 Streszczenie: 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. Afiliacje autorów:
 
117.  Mróz Z., Plaut R.H.^{♦}, On the stability and postcritical behavior of elastic structures with dry friction, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(92)90235L, Vol.29, No.10, pp.12411253, 1992 Streszczenie: 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 postcritical response. Quasistatic 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. Afiliacje autorów:
 
118.  Plaut R.H.^{♦}, Mróz Z., Unidirectional buckling of a pinned elastica with external pressure, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(92)90196Z, Vol.29, No.16, pp.20912100, 1992 Streszczenie: Unidirectional 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. Afiliacje autorów:
 
119.  Pycko S., Mróz Z., Alternative approach to shakedown as a solution of a minmax problem, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01182585, Vol.93, No.1, pp.205222, 1992 Streszczenie: 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 minmax 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 crosssections. Afiliacje autorów:
 
120.  Trąmpczyński W.^{♦}, Mróz Z., Anisotropic hardening model and its application to cyclic loading, International Journal of Plasticity, ISSN: 07496419, DOI: 10.1016/07496419(92)90043C, Vol.8, No.8, pp.925946, 1992 Streszczenie: 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. Afiliacje autorów:
 
121.  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: 07496419, DOI: 10.1016/07496419(92)90049I, Vol.8, No.3, pp.221243, 1992 Streszczenie: 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 stressstrain behaviour. For an associated flow rule the most and least severe restrictions are placed by pure stress control and pure strain control, respectively. Afiliacje autorów:
 
122.  Siemaszko A., Mróz Z., Sensitivity of plastic optimal structures to imperfections and nonlinear geometrical effects, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, ISSN: 1615147X, DOI: 10.1007/BF01743278, Vol.3, No.2, pp.99105, 1991 Streszczenie: The sensitivity of optimal plastic design with respect to geometric imperfections and postcritical 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 twostory frames is analysed in detail. Afiliacje autorów:
 
123.  Siemaszko A., Mróz Z., Sensitivity of optimal structures to imperfections and nonlinear geometrical effects, Structural optimization, ISSN: 09344373, DOI: 10.1007/BF01743278, Vol.3, No.2, pp.99105, 1991 Streszczenie: The sensitivity of optimal plastic design with respect to geometric imperfections and postcritical 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 twostory frames is analysed in detail. Afiliacje autorów:
 
124.  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 MECHANICSTRANSACTIONS OF THE ASME, ISSN: 00218936, DOI: 10.1115/1.2888302, Vol.57, No.1, pp.1824, 1990 Streszczenie: 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 secondorder postbuckling 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 shellofrevolution program. Słowa kluczowe: Oscillating frequencies, Stress, Buckling, Stiffness, Bifurcation, Structural analysis, Computation, Sensitivity analysis, Shells, Virtual work principle Afiliacje autorów:
 
125.  Dems K.^{♦}, Mróz Z., Szeląg D.^{♦}, Optimal design of ribstiffeners in disks and plates, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(89)900176, Vol.25, No.9, pp.973998, 1989 Streszczenie: Disks and plates subjected to stretching and flexure are stiffened by curvilinear ribstiffeners whose shape and crosssectional 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 ringstiffeners in circular disks and plates and of ribstiffeners in a rectangular plate. Afiliacje autorów:
 
126.  Runesson K.^{♦}, Mróz Z., A note on nonassociated plastic flow rules, International Journal of Plasticity, ISSN: 07496419, DOI: 10.1016/07496419(89)900053, Vol.5, No.6, pp.639658, 1989 Streszczenie: 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 PiolaKirchhoff 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. Afiliacje autorów:
 
127.  Mróz Z., Nawrocki P., Deformation and stability of an elastoplastic softening pillar, Rock Mechanics and Rock Engineering, ISSN: 07232632, DOI: 10.1007/BF01583956, Vol.22, No.2, pp.69108, 1989 Streszczenie: A model of rock pillar or coal seam is considered assuming linear elastic behaviour before reaching the maximum strength and postpeak 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 elastoplastic 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. Afiliacje autorów:
 
128.  Mróz Z., Kowalczyk M., Elastoplastic postcritical analysis of disks under tension, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.41, pp.461480, 1989  
129.  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: 15397734, DOI: 10.1080/089054508915650, Vol.17, No.4, pp.431457, 1989 Streszczenie: 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. Afiliacje autorów:
 
130.  Mróz Z., Trąmpczyński W.^{♦}, Hayhurst D.R.^{♦}, Anisotropic creep hardening rule for metals and its application to cyclic loading, International Journal of Plasticity, ISSN: 07496419, DOI: 10.1016/07496419(88)900150, Vol.4, No.3, pp.279299, 1988 Streszczenie: 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 creepplasticity 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. Afiliacje autorów:
 
131.  Dems K.^{♦}, Mróz Z., Variational approach to sensitivity analysis in thermoelasticity, JOURNAL OF THERMAL STRESSES, ISSN: 01495739, DOI: 10.1080/01495738708927014, Vol.10, No.4, pp.283306, 1987  
132.  Dems K.^{♦}, Mróz Z., A Variational Approach to Sensitivity Analysis and Structural Optimization of Plane Arches, Mechanics of Structures and Machines, ISSN: 15397734, DOI: 10.1080/08905458708905121, Vol.15, No.3, pp.297321, 1987 Streszczenie: A plane arch with variable form or crosssectional 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. Afiliacje autorów:
 
133.  Garstecki A.^{♦}, Mróz Z., Optimal Design of Supports of Elastic Structures Subjected to Loads and Initial Distortions, Mechanics of Structures and Machines, ISSN: 15397734, DOI: 10.1080/08905458708905108, Vol.15, No.1, pp.4768, 1987 Streszczenie: 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. Afiliacje autorów:
 
134.  Dems K.^{♦}, Mróz Z., On a class of conservation rules associated with sensitivity analysis in linear elasticity, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(86)901186, Vol.22, No.7, pp.737758, 1986 Streszczenie: 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 pathindependent integrals is derived. It is shown that sensitivity analysis with respect to translation, rotation or expansion of defects can be performed by using these pathindependent integrals. Afiliacje autorów:
 
135.  Petryk H., Mróz Z., Time derivatives of integrals and functionals defined on varying volume and surface domains, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.38, No.56, pp.697724, 1986  
136.  Haftka R.^{♦}, Mróz Z., First and secondorder sensitivity analysis of linear and nonlinearstructures, AIAA Journal, ISSN: 00011452, DOI: 10.2514/3.9412, Vol.24, No.7, pp.11871192, 1986  
137.  Dems K.^{♦}, Mróz Z., Variational approach to first and secondorder sensitivity analysis of elastic structures, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.1620210405, Vol.21, No.4, pp.637661, 1985 Streszczenie: 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 secondorder sensitivity analysis of beams. Afiliacje autorów:
 
138.  Mróz Z., Kamat M.P.^{♦}, Plaut R.H.^{♦}, Sensitivity Analysis and Optimal Design of Nonlinear Beams and Plates, Journal of Structural Mechanics, ISSN: 07836104, DOI: 10.1080/03601218508907500, Vol.13, No.34, pp.245266, 1985 Streszczenie: 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. Afiliacje autorów:
 
139.  Dems K.^{♦}, Mróz Z., Stability Conditions for BrittlePlastic Structures with Propagating Damage Surfaces, Journal of Structural Mechanics, ISSN: 07836104, DOI: 10.1080/03601218508907492, Vol.13, No.1, pp.95122, 1985 Streszczenie: The incremental problem for a brittleplastic 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. Afiliacje autorów:
 
140.  Mróz Z., In Memory of Professor Antoni Sawczuk, Journal of Structural Mechanics, ISSN: 07836104, DOI: 10.1080/03601218508907499, Vol.13, No.34, pp.241243, 1985  
141.  Mróz Z., Trąmpczyński W.^{♦}, On the creephardening rule for metals with a memory of maximal prestress, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(84)900131, Vol.20, No.5, pp.467486, 1984 Streszczenie: The creephardening 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. Afiliacje autorów:
 
142.  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: 00207683, DOI: 10.1016/00207683(84)90026X, Vol.20, No.6, pp.527552, 1984 Streszczenie: 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 pathindependent integrals used in fracture mechanics are rederived as a particular case of general expressions. Afiliacje autorów:
 
143.  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: 00207683, DOI: 10.1016/00207683(83)900641, Vol.19, No.8, pp.677692, 1983 Streszczenie: 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. Afiliacje autorów:
 
144.  Mróz Z., Pietruszczak S., A constitutive model for sand with anisotropic hardening rule, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 03639061, DOI: 10.1002/nag.1610070304, Vol.7, No.3, pp.305320, 1983 Streszczenie: 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. Afiliacje autorów:
 
145.  Pietruszczak S., Mróz Z., On hardening anisotropy of K0consolidated clays, INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, ISSN: 03639061, DOI: 10.1002/nag.1610070105, Vol.7, No.1, pp.1938, 1983 Streszczenie: The combined isotropickinematic hardening rule for clays is presented using the concept of a multisurface model discussed previously in Reference 1. The mechanical behaviour of clays after onedimensional consolidation is next simulated for the axisymmetric stress stress state. A general threedimensional formulation of constitutive relations is also presented. Afiliacje autorów:
 
146.  Zubelewicz A.^{♦}, Mróz Z., Numerical simulation of rock burst processes treated as problems of dynamic instability, Rock Mechanics and Rock Engineering, ISSN: 07232632, DOI: 10.1007/BF01042360, Vol.16, No.4, pp.253274, 1983 Streszczenie: 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. Afiliacje autorów:
 
147.  Lekszycki T., Mróz Z., On Optimal Support Reaction in Viscoelastic Vibrating Structures, Journal of Structural Mechanics, ISSN: 07836104, DOI: 10.1080/03601218308907432, Vol.11, No.1, pp.6779, 1983 Streszczenie: 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. Afiliacje autorów:
 
148.  Mróz Z., Lekszycki T., Optimal support reaction in elastic frame structures, COMPUTERS AND STRUCTURES, ISSN: 00457949, DOI: 10.1016/00457949(81)90002X, Vol.14, No.34, pp.179185, 1981 Streszczenie: 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. Afiliacje autorów:
 
149.  Pietruszczak S., Mróz Z., Finite element analysis of deformation of strainsoftening materials, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.1620170303, Vol.17, No.3, pp.327334, 1981 Streszczenie: A finite element analysis of strainsoftening 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 loaddisplacement curve and the displacement field are not sensitive to the mesh size used in the solution. Afiliacje autorów:
 
150.  Gierliński J.T.^{♦}, Mróz Z., Optimal design of elastic plates and beams taking large deflections and shear forces into account, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01173194, Vol.39, No.1, pp.7792, 1981 Streszczenie: 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. Afiliacje autorów:
 
151.  Mróz Z., Sharma K.G.^{♦}, Finite element applications of viscoplasticity with singular yield surfaces, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.1620150309, Vol.15, No.3, pp.421436, 1980 Streszczenie: The side and corner flow rules for viscoplastic materials with singular yield surfaces are discussed and applied in numerical solution of several boundaryvalue problems. The differences in predictions of displacement and stress fields for different flow rules are demonstrated. Afiliacje autorów:
 
152.  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: 03639061, DOI: 10.1002/nag.1610040104, Vol.4, No.1, pp.4555, 1980 Streszczenie: 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 loadingunloading 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. Afiliacje autorów:
 
153.  Mróz Z., Mironov A.^{♦}, Optimal design of structures for global mechanical constraints, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.32, No.4, pp.505516, 1980  
154.  Kujawski D.^{♦}, Mróz Z., A viscoplastic material model and its application to cyclic loading, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01214633, Vol.36, No.3, pp.213230, 1980 Streszczenie: 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 tensioncompression 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. Afiliacje autorów:
 
155.  Pietruszczak S.^{♦}, Mróz Z., Numerical analysis of elasticplastic compression of pillars accounting for material hardening and softening, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, ISSN: 13651609, DOI: 10.1016/01489062(80)910864, Vol.17, No.4, pp.199207, 1980 Streszczenie: An elasticplastic 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. Afiliacje autorów:
 
156.  Mróz Z., Zagroda B.^{♦}, Analiza nośności ściskanego pasma materiału sprężysto  plastycznego z osłabieniem, Prace IPPT  IFTR Reports, ISSN: 22993657, No.8, pp.159, 1980  
157.  Szeląg D.^{♦}, Mróz Z., Optimal design of vibrating beams with unspecified support reactions, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/00457825(79)90063X, Vol.19, No.3, pp.333349, 1979 Streszczenie: 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. Afiliacje autorów:
 
158.  Masur E.F.^{♦}, Mróz Z., Nonstationary optimality conditions in structural design, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(79)900519, Vol.15, No.6, pp.503512, 1979 Streszczenie: In some cases, optimal structural design corresponds to nonanalytical 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. Afiliacje autorów:
 
159.  Mróz Z., Shamijev F.G.^{♦}, Simplified yield conditions for fibrereinforced plates and shells, ARCHIVES OF CIVIL ENGINEERING, ISSN: 12302945, Vol.25, No.3, pp.463476, 1979  
160.  Dragon A.^{♦}, Mróz Z., A continuum model for plasticbrittle behaviour of rock and concrete, International Journal of Engineering Science, ISSN: 00207225, DOI: 10.1016/00207225(79)900582, Vol.17, No.2, pp.121137, 1979 Streszczenie: The present work deals with a continuum model for timeindependent behaviour of progressively fracturing solids. The rate theory with fracture parameter is discussed and applied to rocklike materials. In particular, elasticbrittle and plasticbrittle idealizations are considered with the fracturing affecting elastic and plastic strains, respectively. The elasticbrittle model incorporates, however, the plasticitylike concept of varying fracture surface. Also the idea of a limit (failure) locus is introduced as the stresspath dependent condition, instead of being prescribed a priori. The plasticity model attempts to cover both stable and unstable portions of the stressstrain 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. Afiliacje autorów:
 
161.  Dragon A.^{♦}, Mróz Z., A model for plastic creep of rocklike materials accounting for the kinetics of fracture, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, ISSN: 13651609, DOI: 10.1016/01489062(79)912002, Vol.16, No.4, pp.253259, 1979 Streszczenie: The constant stress creep behaviour of rocks is studied. A model is presented employing assumption that timedependent microcracking is responsible for the macroscopic viscoplastic deformation. Irreversible volumetric creep is included as the main concern is the material behaviour for stresslevels over the ‘discontinuity’ locus which is identified with the initial yield point. A modified formalism of plasticity theory is used with a scalar crackdensity parameter. The steadystate 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. Afiliacje autorów:
 
162.  Dems K.^{♦}, Mróz Z., Multiparameter structural shape optimization by the finite element method, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.1620130204, Vol.13, No.2, pp.247263, 1978 Streszczenie: 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 nonlinear 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. Afiliacje autorów:
 
163.  Lepik Ü.^{♦}, Mróz Z., Optimal design of impulsively loaded plastic beams for asymmetric mode motions, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(78)900744, Vol.14, No.10, pp.841850, 1978 Streszczenie: Optimal design of a rigidplastic 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]. Afiliacje autorów:
 
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: 03639061, DOI: 10.1002/nag.1610020303, Vol.2, No.3, pp.203221, 1978 Streszczenie: 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 stressspace 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. Afiliacje autorów:
 
165.  Szeląg D.^{♦}, Mróz Z., Optimal Design of Elastic Beams with Unspecified Support Conditions, ZAMMZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 00442267, DOI: 10.1002/zamm.19780581105, Vol.58, No.11, pp.501510, 1978 Streszczenie: 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 crosssections and lengths which are to be determined together with support positions and crosssections. 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. Afiliacje autorów:
 
166.  Michałowski R., Mróz Z., Associated and nonassociated sliding rules in contact friction problems, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.3, pp.259276, 1978  
167.  Lepik Ü.^{♦}, Mróz Z., Optimal design of plastic structures under impulsive and dynamic pressure loading, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(77)900488, Vol.13, No.7, pp.657674, 1977 Streszczenie: Optimal design of a rigidplastic 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. Nonuniqueness of modes is demonstrated and significance of stable mode motions is emphasized. In the second part of the paper, an optimal design of a rigidplastic 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. Afiliacje autorów:
 
168.  Fryze W.^{♦}, Mróz Z., Yield conditions of fiberreinforced materials, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867888X, Vol.25, pp.201234, 1977  
169.  Mróz Z., Pietruszczak S., Description of polymer impregnated concrete, ARCHIVES OF CIVIL ENGINEERING, ISSN: 12302945, Vol.23, pp.107124, 1977  
170.  Mróz Z., Pietruszczak S., Flexure and extension of concrete beams with polymer impregnated external layers, ARCHIVES OF CIVIL ENGINEERING, ISSN: 12302945, Vol.23, pp.125144, 1977  
171.  Szymański Cz.^{♦}, Mróz Z., Analiza procesów mechanicznych w materiale rozdrobnionym w operacjach napełniania i opróżniania kanałów zbieżnych, Prace IPPT  IFTR Reports, ISSN: 22993657, No.32, pp.1163, 1977  
172.  Mróz Z., Shrivastava H.P.^{♦}, Dubey R.N.^{♦}, A nonlinear hardening model and its application to cyclic loading, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01176929, Vol.25, No.1, pp.5161, 1976 Streszczenie: By modifying the translational rule in a nonlinear, 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 loadingunloading or cyclic loading tests. Afiliacje autorów:
 
173.  Grzymkowski M.^{♦}, Mróz Z., Slipline solutions of axisymmetric problems of plate compression, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867888X, Vol.24, pp.171183, 1976  
174.  Dragon A.^{♦}, Mróz Z., On the plasticbrittle behaviour of rock and concrete, Mechanics Research Communications, ISSN: 00936413, DOI: 10.1016/00936413(76)901063, Vol.3, No.5, pp.429434, 1976  
175.  Mróz Z., Raniecki B., A derivation of the uniqueness conditions in coupled thermoplasticity, International Journal of Engineering Science, ISSN: 00207225, DOI: 10.1016/00207225(76)900124, Vol.14, No.4, pp.395401, 1976 Streszczenie: 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. Afiliacje autorów:
 
176.  Mróz Z., Raniecki B., On the uniqueness problem in coupled thermoplasticity, International Journal of Engineering Science, ISSN: 00207225, DOI: 10.1016/00207225(76)900902, Vol.14, No.2, pp.211221, 1976 Streszczenie: 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. Afiliacje autorów:
 
177.  Mróz Z., Garstecki A.^{♦}, Optimal design of structures with unspecified loading distribution, Journal of Optimization Theory and Applications, ISSN: 00223239, DOI: 10.1007/BF00933629, Vol.20, No.3, pp.359380, 1976 Streszczenie: 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. Słowa kluczowe: Structural optimization, engineering design, optimality conditions, calculus of variations, structural mechanics Afiliacje autorów:
 
178.  Mróz Z., Lind N.C.^{♦}, Simplified theories of cyclic plasticity, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01170622, Vol.22, No.1, pp.131152, 1975 Streszczenie: 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. Afiliacje autorów:
 
179.  Mróz Z., Rozvany G.I.N.^{♦}, Optimal design of structures with variable support conditions, Journal of Optimization Theory and Applications, ISSN: 00223239, DOI: 10.1007/BF00933023, Vol.15, No.1, pp.85101, 1975 Streszczenie: 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 positiondependent cost of support into the design procedure. Both rigid and flexible or yielding supports are considered. Słowa kluczowe: Structural optimization, engineering design, optimality conditions, calculus of variations, structural mechanics Afiliacje autorów:
 
180.  Mróz Z., Taylor J.E.^{♦}, Prestress for maximum strength, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(73)900589, Vol.9, No.12, pp.15351541, 1973 Streszczenie: The problem of designing prestress to maximize elastic capacity is treated analytically. Our formulation models structures comprised of a onematerial elastic continuum, subject to a single deterministic load configuration. Afiliacje autorów:
 
181.  Shrivastava H.P.^{♦}, Mróz Z., Dubey R.N.^{♦}, Yield criterion and secondorder effects in planestress, ACTA MECHANICA, ISSN: 00015970, DOI: 10.1007/BF01260885, Vol.17, No.1, pp.137143, 1973 Streszczenie: 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 tensiontorsion loading the yield surface is nonsymmetric with respect to the torsional stress axis. Due to the nonsymmetry, the yield condition describes the secondorder effect relating to axialstrain accumulation in cyclic torsion, and at the same time it has got a very simple form compared to other yield conditions describing this effect. Afiliacje autorów:
 
182.  Mróz Z., Raniecki B., Variational principles in uncoupled thermoplasticity, International Journal of Engineering Science, ISSN: 00207225, DOI: 10.1016/00207225(73)900803, Vol.11, No.11, pp.11331141, 1973 Streszczenie: Stressrate and strainrate 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. Afiliacje autorów:
 
183.  Mróz Z., Drescher A., Hueckel T., Doskonalenie metod badania parametrów płynięcia materiałów ziarnistych, Prace IPPT  IFTR Reports, ISSN: 22993657, No.54, pp.1130, 1973  
184.  Mróz Z., Goss Cz.^{♦}, O złożonych modelach wzmocnienia plastycznego, Mechanika Teoretyczna i Stosowana, ISSN: 00793701, Vol.2, No.10, pp.259279, 1972  
185.  Mróz Z., Kwaszczyńska K., Some boundary value problems for density hardening materials, Rozprawy Inżynierskie, ISSN: 0867888X, Vol.19, pp.1542, 1971  
186.  Mróz Z., Szymański Cz.^{♦}, A simplified theory of flow of granular materials in converging channels, Archiwum Inżynierii Lądowej, ISSN: 12302945, Vol.17, pp.555578, 1971  
187.  Kozłowski W.^{♦}, Mróz Z., Optimal design of disks subject to geometric constraints, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 00207403, DOI: 10.1016/00207403(70)900299, Vol.12, No.12, pp.10071021, 1970 Streszczenie: 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 semiplane below the line joining supports or within a strip of prescribed width. Afiliacje autorów:
 
188.  Mróz Z., Optimal design of structures of composite materials, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(70)900016, Vol.6, No.7, pp.859870, 1970 Streszczenie: 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. Afiliacje autorów:
 
189.  Mróz Z., Optimal Design of Elastic Structures Subjected to Dynamic, HarmonicallyVarying Loads, ZAMMZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 00442267, DOI: 10.1002/zamm.19700500505, Vol.50, No.5, pp.303309, 1970 Streszczenie: Optimal design of elastic structures subjected to one or several dynamic, harmonicallyvarying 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 boundaryvalue problems. Afiliacje autorów:
 
190.  Mróz Z., Szymański Cz.^{♦}, Uproszczona teoria przepływu ośrodków rozdrobnionych w zbieżnych kanałach, Prace IPPT  IFTR Reports, ISSN: 22993657, No.50, pp.142, 1970  
191.  Kwaszczyńska K., Mróz Z., Drescher A., Analysis of compression of short cylinders of Coulomb material, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 00207403, DOI: 10.1016/00207403(69)900010, Vol.11, No.2, pp.145158, 1969 Streszczenie: 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 HaarKármán hypothesis is satisfied. The solution is obtained for several heightdiameter ratios, various friction conditions at the cylinderplate 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. Afiliacje autorów:
 
192.  Kozłowski W.^{♦}, Mróz Z., Optimal design of solid plates, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/00207683(69)900456, Vol.5, No.8, pp.781794, 1969 Streszczenie: 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. Afiliacje autorów:
 
193.  Mróz Z., Drescher A., Limit Plasticity Approach to Some Cases of Flow of Bulk Solids, Journal of Engineering for Industry, ISSN: 00221817, DOI: 10.1115/1.3591573, Vol.91, No.2, pp.357364, 1969 Streszczenie: Depending on the stress state, a bulk solid, regarded as the elasticplastic 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. Słowa kluczowe: Flow (Dynamics), Plasticity, Bulk solids, Coulombs, Critical points (Physics), Stress, Surface roughness, Motion, Theorems (Mathematics), Pressure Afiliacje autorów:
 
194.  Mróz Z., Optymalizacja konstrukcji z materiałów wielofazowych, Prace IPPT  IFTR Reports, ISSN: 22993657, No.15, pp.121, 1969  
195.  Mróz Z., An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model, TRIBOLOGY LETTERS, ISSN: 10238883, DOI: 10.1007/BF01176668, Vol.7, No.2, pp.199212, 1969 Streszczenie: 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 workhardening 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. Afiliacje autorów:
 
196.  Mróz Z., Kwaszczyńska K., Axially symmetric plastic flow of metals treated by the graphical methods, Archiwum Inżynierii Lądowej, ISSN: 12302945, Vol.14, pp.2737, 1968  
197.  Kwaszczyńska K., Mróz Z., Drescher A., Analiza ściskania krótkich walców z materiału Coulomba, Prace IPPT  IFTR Reports, ISSN: 22993657, No.29, pp.146, 1968  
198.  Mróz Z., On the description of anisotropic workhardening, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 00225096, DOI: 10.1016/00225096(67)900300, Vol.15, No.3, pp.163175, 1967 Streszczenie: 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. Afiliacje autorów:
 
199.  Mróz Z., Graphical solution of axially symmetric problems of plastic flow, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK ZAMP, ISSN: 00442275, DOI: 10.1007/BF01596914, Vol.18, No.2, pp.219236, 1967 Streszczenie: 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 CoulombTresca et à l'hypothèse du potentiel plastique. Deux cas ont été considérés: d'une part des régimes de HaarKármán 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. Afiliacje autorów:
 
200.  Mróz Z., Kwaszczyńska K., Plastic compression of short cylinders between rigid plates, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.19, 1967  
201.  Drescher A., Kwaszczyńska K., Mróz Z., Statics and kinematics of the granular medium in the case of wedge indentation, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.19, pp.99113, 1967  
202.  Mróz Z., On the optimum design of reinforced slabs, TRIBOLOGY LETTERS, ISSN: 10238883, DOI: 10.1007/BF01193599, Vol.3, No.1, pp.3455, 1967 Streszczenie: A problem of optimum design of reinforced slabs is analyzed assuming a rigid, perfectlyplastic 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 nonsymmetric loading are considered in order to illustrate the theory. Afiliacje autorów:
 
203.  Mróz Z., On forms of constitutive laws for elasticplastic solids, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.18, No.1, pp.335, 1966  
204.  Mróz Z., Admissible loading paths in the deformation theories of plasticity, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.16, 1964  
205.  Mróz Z., Bingye X.^{♦}, The load carrying capacities of symmetrically loaded spherical shells, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.15, pp.245266, 1963  
206.  Mróz Z., Limit analysis of plastic structures subject to boundary variations, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, No.15, pp.6376, 1963  
207.  Mróz Z., Nonassociated flow laws in plasticity, Journal de mécanique, ISSN: 00217832, Vol.2, pp.2142, 1963  
208.  Mróz Z., On a problem of minimum weight design, Quarterly of Applied Mathematics, ISSN: 15524485, DOI: 10.1090/qam/135327, Vol.19, pp.127135, 1961 Streszczenie: 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. Afiliacje autorów:
 
209.  Mróz Z., The loadcarrying capacity of orthotropic shells, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.12, pp.85107, 1960  
210.  Mróz Z., Plastic deformation of annular plates under dynanic loads, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.10, pp.499516, 1958  
211.  Olszak W., Mróz Z., Note on the completeness of elasticplastic solution to certain boundaryvalue problems for the eccentric ring, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, Vol.10, pp.441444, 1958  
212.  Mróz Z., The load carrying capacity and minimum weight design of annular plates, Rozprawy Inżynierskie, ISSN: 0867888X, Vol.4, pp.605625, 1958  
213.  Mróz Z., Limit analysis and optimal design of annular plates, Rozprawy Inżynierskie, ISSN: 0867888X, pp.605626, 1958  
214.  Olszak W., Mróz Z., Elastic bending of circular plates with eccentric holes /application of the method of inversion/, ARCHIWUM MECHANIKI STOSOWANEJ, ISSN: 03732029, 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.1720, 1989 
2. 29  Derski W., Izbicki R.^{♦}, Kisiel I.^{♦}, Mróz Z., Mechanika skał i gruntów, PWN, Seria Mechanika Techniczna, t. 7, pp.1573, 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.146, 2003), pp.146, 2017 
2. 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.281312, 2016 
3. 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 NiPt w świecach zapłonowych w silnikach na biopaliwo, Politechnika Świętokrzyska, Kielce, pp.2233, 2016 
4. 538  Dems K.^{♦}, Mróz Z., Encyclopedia of Thermal Stresses, rozdział: Sensitivity Analysis for Thermoelastic State Fields, Springer Netherlands, pp.42904300, 2014 
5. 279  Maciejewski J., Białas M., Mróz Z., 6th European Congress on Computational Methods in Applied Sc. and Engng. (ECCOMAS 2012), September 1014, 2012, Vienna, Austria, rozdział: Modelling of contact interface oxidation process at asperity scale, University of Vienna, Austria, pp.18, 2012 
6. 40  Mróz Z., Maciejewski J., Bifurcations, Instabilities and Degradations in Geomaterials, rozdział: Critical Plane Approach to Analysis of Failure Criteria for Anisotropic Geomaterials, SpringerVerlag Berlin Heidelberg, pp.6989, 2011 
7. 41  Maciejewski J., Mróz Z., Bifurcations, Instabilities and Degradations in Geomaterials, rozdział: Analysis of Deformation and Damage Processes in SoilTool Interaction Problems, SpringerVerlag Berlin Heidelberg, pp.325345, 2011 
8. 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.213270, 2005 
9. 180  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.95139, 2005 
10. 545  Mróz Z., Comprehensive Structural Integrity, rozdział: 2.01  Strength Theories, Elsevier B.V., 2: Fundamental Theories and Mechanisms of Failure, pp.146, 2003 
11. 525  Mróz Z., Białas M., IUTAM Symposium on Analytical and Computational Fracture Mechanics of NonHomogeneous Materials, rozdział: Modeling of Progressive Interface Failure Under Monotonic and Cyclic Loading, Springer, Dordrecht, series Solid Mechanics and its Applications, 97, pp.211222, 2002 
12. 526  Sadowski T.^{♦}, Samborski S.^{♦}, Mróz Z., IUTAM Symposium on Analytical and Computational Fracture Mechanics of NonHomogeneous Materials, rozdział: Gradual Degradation of Initially Porous Polycrystalline Ceramics Subjected to QuasiStatic Tension, Springer, Dordrecht, series Solid Mechanics and its Applications, 97, pp.401405, 2002 
13. 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.179186, 2002 
14. 536  Mróz Z., Friction and Instabilities, rozdział: Contact Friction Models and Stability Problems, Springer Vienna, series International Centre for Mechanical Sciences, 457, pp.179232, 2002 
15. 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.489498, 1999 
16. 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.145162, 1998 
17. 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.6982, 1997 
18. 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.318, 1995 
19. 535  Mróz Z., Stupkiewicz S., IUTAM Symposium on MicrostructureProperty Interactions in Composite Materials, rozdział: Hysteretic Effects and Progressive Delamination at Composite Interfaces, Springer Netherlands, series Solid Mechanics and its Applications, 37, pp.247264, 1995 
20. 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.349380, 1995 
21. 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.455476, 1993 
22. 543  Mróz Z., Dems K.^{♦}, Optimal Design with Advanced Materials, rozdział: Discrete and continuous reinforcement of materials and structures, Elsevier B.V., pp.383405, 1993 
23. 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.353370, 1991 
24. 540  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.255266, 1988 
25. 530  HolnickiSzulc J., Mróz Z., Structural Control, rozdział: Active Control of Stresses and Deflections of Elastic Structures by Means of Imposed Distortions, Springer Netherlands, pp.297317, 1987 
26. 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.79110, 1986 
27. 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.597622, 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.1502, 1995 
Prace konferencyjne
1.  Mróz K.P., Mróz Z., Doliński K., Mixed mode crack growth conditions  critical plane approaches, ECF19, 19th European Conference on Fracture, 20120826/0831, Kazan (RU), pp.18, 2012 Streszczenie: The crack growth rules are usually specified in terms of the potential energy release or of non local stress or strain criteria. In the present work, the criteria based on the critical plane concept are first discussed and expressed in terms of averaged stress developed in the crack front domain. The transition from tensile to shear fracture is predicted for varying mode mixity ratio. Słowa kluczowe: mixed mode crack growth, critical plane, energy conditions, brittle fracture, ductile fracture, SIF, strain energy density, LEFM Afiliacje autorów:
 
2.  Maciejewski G., Mróz Z., Optimization of functionally gradient materials under cyclic thermal and mechanical loading, International Conference Numerical Heat Transfer, 20120904/0906, Wrocław (PL), pp.421430, 2012 Streszczenie: The robust and simple optimization method of FGM is proposed for combined cyclic thermal and mechanical loading. Słowa kluczowe: thermomechanical analysis, highcycle loading, coating, FGM, optimization Afiliacje autorów:
 
3.  Páczelt I.^{♦}, Mróz Z., Numerical Analysis of ThermoMechanical Wear Problems for Reciprocal Punch Sliding, CivilComp Proceedings, ISSN: 17593433, DOI: 10.4203/ccp.99.146, No.146, 2012 Streszczenie: The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. The transient process tends to a steady state occuring at fixed contact stress and strain distribution. This state corresponds to the minimum of the wear dissipation power. The optimality conditions of the functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. This paper extends the previous analyses [1,2,3,4,5] of the steady state conditions to cases of periodic sliding of contacting bodies, assuming cyclic steady state conditions for both mechanical and thermal fields. Słowa kluczowe: contact problems, sliding wear, heat generation, steadystate, periodic sliding, optimal contact surface, pversion of finite elements Afiliacje autorów:
 
4.  Mróz K.M., Mróz Z., Crack growth modes in inhomogeneous materials: analysis of biand multimaterial interfaces, 1st International Conference on Characterisation of Crack Tip Stress Fields, 20110307/0309, Forni di Sopra (IT), pp.1725, 2011 Streszczenie: Most structural components contain inhomogeneities such as hardened surface layers or coatings, welded or bonded elements, etc. The crack growth mode then depends not only on applied loading and structure geometry but also on material inhomogeneity. In the presentation the analysis of crack growth mode will be discussed for two cases: a bimaterial structure with two materials of different thermoelastic and plastic properties connected along the interface and a structure with introduced interlayer of different material. The simplified approach is presented, namely the MK criterion [1,2] based on the linear elastic fracture mechanics (LEFM). In the criterion it is assumed that crack growth follows the direction of minimum distortion energy density at a distance corresponding to specified value of dilatation energy. For two materials, A and B the crack growth from A to B or along the interface AB may occur depending on relative critical stress and fracture energy values. For a threephases structure, various modes of crack growth are possible. Słowa kluczowe: SIF, Strain energy density, LEFM, Fracture, Bimaterial, Layers, Fatigue crack growth Afiliacje autorów:
 
5.  Mróz K.P., Mróz Z., Doliński K., Kryterium energetyczne wzrostu krzywoliniowej trajektorii szczeliny, Zeszyty Naukowe Politechniki Opolskiej, ISSN: 14296055, Vol.343, pp.116119, 2011 Streszczenie: W pracy rozważono możliwość odchylania się szczeliny dla przypadku gdy KI>0, KII≥0 w dwuosiowym stanie obciążenia. Do analizy wykorzystano dwa kryteria liniowej sprężystej mechaniki pękania (LSMP) uwzględniając efekt naprężenia T: klasyczne kryterium maksymalnych naprężeń obwodowych (MNO) oraz energetyczne kryterium MK [7,8,9]. Przedstawiono po równanie obu kryteriów w odniesieniu do niestabilnego kierunku p ropagacji szczeliny, definiowanego w pracy jako odchylenie się ścieżki propagacji od płaszczyzny początkowej lokalizacji szczeliny. Przedstawiono również porównanie przypadków granicznych z wykorzystaniem modeli wzrostu początkowej szczeliny. Afiliacje autorów:
 
6.  Białas M., Mróz Z., An energy model of segmentation cracking of SiOX thin film on a polymer substrate, 31st International Conference on Advanced Ceramics and Composites, 20070121/0126, Daytona Beach (US), DOI: 10.1002/9780470339510.ch23, Vol.28, No.3, pp.231242, 2007 Słowa kluczowe: segmentation cracking, thin films, polymer substrate, energy transition, polyethylene terephthalate Afiliacje autorów:
 
7.  Boukpeti N.^{♦}, Mróz Z., Drescher A.^{♦}, Rate Effects in the Superior Sand Model, First JapanU.S. Workshop on Testing, Modeling, and Simulation, 20030627/0629, Boston (US), DOI: 10.1061/40797(172)6, pp.123135, 2003 Streszczenie: This paper aims at analyzing the response of the elastoviscoplastic model Superior sand proposed by Boukpeti et al. for describing rate effects in undrained loading of looselypacked granular deposits. The equations governing the model in triaxial compression are solved for three loading histories: constant strain rate, constant stress rate, and creep. The resulting stressstraintime curves are discussed in the light of material instability states in relation to static liquefaction. It is shown that the classical secondorder work rate instability criterion is no longer valid, and a new criterion based on the deformation acceleration is presented. Afiliacje autorów:
 
8.  Mróz Z., Seweryn A.^{♦}, Nonlocal failure and damage evolution rule : Application to a dilatant crack model, JOURNAL DE PHYSIQUE IV, ISSN: 11554339, DOI: 10.1051/jp4:1998832, Vol.8, No.PR8, pp.Pr8257Pr8268, 1998 Streszczenie: A nonlocal crack propagation and damage evolution criteria were discussed in detail by the authors in [1315] and applied to predict crack initiation from sharp notches and damage accumulation for complex cyclic loading programs. In the present paper the nonlocal condition is applied to the case of a cracked body subjected to compression and shear tractions inducing frictional slip and dilatancy at crack interfaces. The crack propagation directions with critical loading conditions are obtained taking into account the crack asperity interaction and dilatancy induced by slip. The material strength and compliance variation can be predicted from the model. Afiliacje autorów:
 
9.  Sergeyev O., Mróz Z., Optimal joint positions and stiffness distribution for minimum mass frames with damping constraints, Structural optimization, ISSN: 09344373, DOI: 10.1007/BF01271430, Vol.16, No.4, pp.231245, 1998 Streszczenie: Optimal design of frames including crosssectional dimensions (size parameters) and rigid joint positions between beams (configuration parameters) is treated in the paper. The optimal design corresponds to a minimal mass structure with constraints set on damping capacity of free vibration modes. The sensitivity analysis of distinct as well as multiple frequencies is performed analytically using a complex variable sensitivity method. The linking process of size and configuration variables is applied to generate different classes of optimal designs. The numerical algorithm is based on quadratic approximation of the objective function and linear approximation of active constraints. The examples are provided for 2, 12, and 124 beam frames. Afiliacje autorów:
 
10.  Bojczuk D.^{♦}, Mróz Z., On optimal design of supports in beam and frame structures, Structural optimization, ISSN: 09344373, DOI: 10.1007/BF01213999, Vol.16, No.1, pp.4757, 1998 Streszczenie: An algorithm of optimal design of supports including their number, position and stiffness is proposed. The number of supports constitute topological design parameters, their positions correspond to configuration parameters. Both, elastic and rigid supports are considered and the optimization is aimed to minimize the total structure cost. The topology bifurcation points correspond to generation of new supports. The topological sensitivity derivative is used in deriving the optimality conditions Afiliacje autorów:
 
11.  Mróz Z., Seweryn A.^{♦}, Damage Description with Related Crack Initiation and Propagation Conditions, JOURNAL DE PHYSIQUE IV, ISSN: 11554339, DOI: 10.1051/jp4:1996653, Vol.6, No.C6, pp.C6529C6538, 1996 Streszczenie: The damage accumulation condition expressed in terms of traction components on a physical plane is considered for both monotonic and cyclic loading conditions. The crack initiation is assumed to correspond to a critical value of damage parameter on a maximum damage plane. A nonlocal condition is formulated for singular stress or strain regimes. The model is applied to predict damage distribution within the element for cyclic loading condition ; in particular for combined torsion and bending. The damage tensors are introduced to describe the predicted damage distribution. Afiliacje autorów:
 
12.  Masur E.F.^{♦}, Mróz Z., Singular Solutions in Structural Optimization Problems, IUTAM Symposium on Variational Methods in the Mechanics of Solids, 19780911/0913, Evanston (US), DOI: 10.1016/B9780080247281.500598, pp.337343, 1980 Streszczenie: The application of standard stationarity conditions to the optimal design of a structure against buckling (or other eigenvalue constraints) may actually lead to a reduction of its real strength in the sense that the “optimized” structure has been weakened with respect to higher modes to the extent that these have now become fundamental. In this case a true optimum occurs when the magnitudes of several eigenvalues coalesce, and the corresponding optimality condition is then no longer stationary. This singular condition is derived and applied to several examples of major practical significance, together with a method of obtaining an approximate solution to the resulting set of nonlinear equations. Afiliacje autorów:
 
13.  Mróz Z., Mode Approach to Rational Synthesis of Structures under Impulsive and Dynamic Pressure Loading, SMiRT, 4th International Conference on Structural Mechanics in Reactor Technology, 19770613/0613, San Francisco (US), pp.L2/41L2/48, 1977  
14.  Mróz Z., Boundary Value Problems in Cyclic Plasticity, SMIRT, 2nd International Conference on Structural Mechanics in Reactor Technology, 19730910/0914, Berlin (DE), pp.L7/61L7/67, 1973  
15.  Mróz Z., On the Theory of Steady Plastic Cycles in Structures, SMiRT, 1st International Conference on Structural Mechanics in Reactor Technology, 19710920/0924, Berlin (DE), pp.489501, 1971 
Abstrakty konferencyjne
1.  Páczelt I.^{♦}, Mróz Z., Analysis of steady wear states for monotonic and periodic sliding, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.283284, 2014  
2.  Maciejewski G., Mróz Z., The robust optimization method of functionally gradient materials under cyclic thermal and mechanical loading, ECCOMAX 2012, 6th European Congress on Computational Methods in Applied Sciences and Engineering, 20120910/0914, Wiedeń (AT), pp.12, 2012 Słowa kluczowe: FGM, optimization, thermomechanical analysis, coating, highcycle loading Afiliacje autorów:
 
3.  Maciejewski J., Białas M., Mróz Z., Two scale modelling of wear and oxidation processes, FRICTION 2012, VII International Conference, Modelling And Simulation Of The Friction Phenomena In The Physical And Technical Systems, 20120522/0522, Warszawa (PL), 2012  
4.  Maciejewski J., Białas M., Mróz Z., Evolution of friction coefficient in the tribological test, XX FRENCHPOLISH SEMINAR OF MECHANICS, 20120512/0512, Warszawa (PL), 2012  
5.  Maciejewski J., Mróz Z., Deformation response of geomaterial interfaces coupled with progressive damage and wear, SolMech 2010, 37th Solid Mechanics Conference, 20100906/0910, Warszawa (PL), pp.248, 2010  
6.  KowalczykGajewska K., Mróz Z., Pęcherski R.B., Micromechanical modeling of polycrystalline materials under nonproportional deformation paths, SolMech 2006, 35th Solid Mechanics Conference, 20060904/0908, Kraków (PL), pp.213214, 2006 