prof. dr hab. inż. Stanisław Stupkiewicz 

Doktorat
19961128  Modelowanie poślizgów i rozwoju uszkodzeń w strefie kontaktu ciał sprężystoplastycznych
 524 
Habilitacja
Profesura
20111205  Nadanie tytułu naukowego profesora 
Promotor prac doktorskich
1.  20090226  Sadowski Przemysław  Modelowanie przepływu ciepła przez powierzchnię kontaktu ciał chropowatych w procesach przeróbki plastycznej  627  
2.  20090122  Lengiewicz Jakub  Analiza wrażliwości dla zagadnień kontaktowych z tarciem  621 
Ostatnie publikacje
1.  Sadowski P., KowalczykGajewska K., Stupkiewicz S., Consistent treatment and automation of the incremental Mori–Tanaka scheme for elastoplastic composites, COMPUTATIONAL MECHANICS, ISSN: 01787675, DOI: 10.1007/s004660171418z, pp.119, 2017 Streszczenie: A consistent algorithmic treatment of the incremental Mori–Tanaka (MT) model for elastoplastic composites is proposed. The aim is to develop a computationally efficient and robust micromechanical constitutive model suitable for largescale finiteelement computations. The resulting overall computational scheme is a doublynested iterationsubiteration scheme. The Newton method is used to solve the nonlinear equations at each level involved. Exact linearization is thus performed at each level so that a quadratic convergence rate can be achieved. To this end, the automatic differentiation (AD) technique is used, and the corresponding ADbased formulation is provided. Excellent overall performance of the present MT scheme in threedimensional finiteelement computations is illustrated. Słowa kluczowe: Mori–Tanaka method, Composite materials, Elastoplasticity, Finite element method, Automatic differentiation Afiliacje autorów:
 45p.  
2.  Petryk H., Stupkiewicz S., Kucharski S., On direct estimation of hardening exponent in crystal plasticity from the spherical indentation test, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/j.ijsolstr.2016.09.025, Vol.112, pp.209221, 2017 Streszczenie: A novel methodology is proposed for estimating the strain hardening exponent of a metal single crystal directly from the spherical indentation test, without the need of solving the relevant inverse problem. The attention is focused on anisotropic pilingup and sinkingin that occur simultaneously in different directions, in contrast to the standard case of axial symmetry for isotropic materials. To correlate surface topography parameters with the value of material hardening exponent, a finiteelement study of spherical indentation has been performed within a selected penetration depth range using a finitestrain crystal plasticity model. It is shown how the powerlaw hardening exponent can be estimated from the measured pileup/sinkin pattern around the residual impression after indentation in a (001)oriented fcc single crystal of a small initial yield stress. For this purpose, a new parameter of surface topography is defined as the normalized material volume displaced around the nominal contact zone, calculated by integration of the local residual height (positive or negative) over a centered circular ring. That indicator can be easily determined from an experimental topography map available in a digital form. Comparison is made with the estimates based on measurements of the contact area and the slope of the load–penetration depth curve in logarithmic coordinates. The proposed methodology is extended to estimation of the hardening exponent simultaneously with the initial yield stress when the latter is not negligible. Experimental verification for a Cu single crystal leads to promising conclusions. Słowa kluczowe: Metal crystal, Elastoplasticity, Finite deformation, Strain hardening, Experimental identification Afiliacje autorów:
 35p.  
3.  Sadowski P., KowalczykGajewska K., Stupkiewicz S., Response discontinuities in the solution of the incremental Mori–Tanaka scheme for elastoplastic composites, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.69, No.1, pp.327, 2017 Streszczenie: The incremental Mori–Tanaka model of elastoplastic composites is discussed, and the corresponding finitestep formulation is shown to lead to discontinuities in the overall response at the instant of elastictoplastic transition in the matrix. Specifically, two situations may be encountered: the incremental equations may have two solutions or no solution. In the former situation, switching between the two solutions is associated with a jump in the overall stress. Response discontinuities are studied in detail for a special case of proportional deviatoric loading. The discontinuities constitute an undesirable feature of the incremental Mori–Tanaka scheme that apparently has not been discussed in the literature so far. Remedies to the related problems are briefly discussed. Słowa kluczowe: meanfield homogenization, Mori–Tanaka method, incremental scheme, composite materials, elastoplasticity Afiliacje autorów:
 25p.  
4.  Tůma K., Stupkiewicz S., Petryk H., Size effects in martensitic microstructures: Finitestrain phase field model versus sharpinterface approach, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 00225096, DOI: 10.1016/j.jmps.2016.04.013, Vol.95, pp.284307, 2016 Streszczenie: A finitestrain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharpinterface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phasefield approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two orderparameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, sizedependent microstructures with diffuse interfaces are calculated for the cubictoorthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharpinterface microstructures with interfacial energy effects. Słowa kluczowe: Phasefield method, Microstructure, Martensite, Size effects, Shape memory alloys Afiliacje autorów:
 40p.  
5.  Temizer I.^{♦}, Stupkiewicz S., Formulation of the Reynolds equation on a timedependent lubrication surface, PROCEEDINGS OF THE ROYAL SOCIETY AMATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN: 13645021, DOI: 10.1098/rspa.2016.0032, Vol.472, No.20160032, pp.116, 2016 Streszczenie: The Reynolds equation, which describes the lubrication effect arising through the interaction of two physical surfaces that are separated by a thin fluid film, is formulated with respect to a continuously evolving third surface that is described by a timedependent curvilinear coordinate system. The proposed formulation essentially addresses lubrication mechanics at interfaces undergoing large deformations and a priori satisfies all objectivity requirements, neither of which are features of the classical Reynolds equation. As such, this formulation may be particularly suitable for nonstationary elastohydrodynamic lubrication problems associated with soft interfaces. The ability of the formulation to capture finitedeformation effects and the influence of the choice of the third surface are illustrated through analytical examples. Słowa kluczowe: Reynolds equation, elastohydrodynamic lubrication, soft interfaces, timedependent curvilinear coordinates, finite deformations, objectivity Afiliacje autorów:
 35p.  
6.  Tůma K., Stupkiewicz S., Phasefield study of sizedependent morphology of austenite–twinned martensite interface in CuAlNi, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/j.ijsolstr.2016.07.040, Vol.9798, pp.89100, 2016 Streszczenie: Sizedependent microstructure of the interface layer between austenite and twinned martensite is studied using a recently developed finitestrain phasefield model. The microstructure is assumed periodic and twodimensional, however, nonzero outofplane displacements are allowed so that the basic microstructural features, specifically the nominal orientation of the twinning and habit planes and the twin fraction, are consistent with the crystallographic theory of martensite. The phasefield computations are carried out for the CuAlNi shape memory alloy undergoing the cubictoorthorhombic transformation, and the corresponding four crystallographically distinct microstructures of the austenite–twinned martensite interface are studied in detail. The focus is on sizedependent morphology of the interface layer and on sizedependent interfacial and elastic microstrain energy contributions. Two mechanisms of reducing the elastic microstrain energy are revealed: formation of a nonplanar zigzaglike interface and twin branching. Słowa kluczowe: Microstructure, Phase transformation, Martensite, Phasefield method, Size effects Afiliacje autorów:
 35p.  
7.  Stupkiewicz S., Lengiewicz J., Sadowski P., Kucharski S., Finite deformation effects in soft elastohydrodynamic lubrication problems, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2015.03.016, Vol.93, pp.511522, 2016 Streszczenie: Soft elastohydrodynamic lubrication regime is typical for many elastomeric and biological contacts. As one or both contacting bodies are then highly compliant, relatively low contact pressures may lead to large deformations which are neglected in the classical EHL theory. In the paper, the related finitedeformation effects are studied for two representative softEHL problems. To this end, a fullycoupled nonlinear formulation has been developed which combines finitestrain elasticity for the solid and the Reynolds equation for the fluid, both treated using the finite element method with full account of all elastohydrodynamic couplings. Results of friction measurements are also reported and compared to theoretical predictions for lubricated contact of a rubber ball sliding against a steel disc under high loads. Słowa kluczowe: SoftEHL problem, Finite deformation, Finite element method, Monolithic scheme Afiliacje autorów:
 35p.  
8.  Petryk H., Stupkiewicz S., A minimal gradientenhancement of the classical continuum theory of crystal plasticity. Part I: The hardening law, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.68, No.6, pp.459485, 2016 Streszczenie: A simple gradientenhancement of the classical continuum theory of plasticity of single crystals deformed by multislip is proposed for incorporating size effects in a manner consistent with phenomenological laws established in materials science. Despite considerable efforts in developing gradient theories, there is no consensus regarding the minimal set of physically based assumptions needed to capture the slipgradient effects in metal single crystals and to provide a benchmark for more refined approaches. In order to make a step towards such a reference model, the concept of the tensorial density of geometrically necessary dislocations generated by sliprate gradients is combined with a generalized form of the classical Taylor formula for the flow stress. In the governing equations in the rate form, the derived internal length scale is expressed through the current flow stress and standard parameters so that no further assumption is needed to define a characteristic length. It is shown that this internal length scale is directly related to the mean free path of dislocations and possesses physical interpretation which is frequently missing in other gradientplasticity models. Słowa kluczowe: gradient plasticity, geometrically necessary dislocations, single crystal, strainhardening, internal length scale, size effect Afiliacje autorów:
 25p.  
9.  Stupkiewicz S., Petryk H., A minimal gradientenhancement of the classical continuum theory of crystal plasticity. Part II: Size effects, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.68, No.6, pp.487513, 2016 Streszczenie: In our previous paper, a simple gradientenhancement of the classical continuum theory of plasticity of single crystals deformed by multislip has been proposed for incorporating size effects. A single internal length scale has been derived as an explicit function of the flow stress defined as the isotropic part of critical resolved shear stresses. The present work is focused on verification whether the simplifications involved are not too severe and allow satisfactory predictions of size effects. The model has been implemented in a finite element code and applied to threedimensional simulations of fcc single crystals. We have found that the experimentally observed indentation size effect in a Cu single crystal is captured correctly in spite of the absence of any adjustable lengthscale parameter. The finite element treatment relies on introducing nonlocal slip rates that average and smoothen on an element scale the corresponding local quantities. Convergence of the finite element solution to the analytical one is also verified for the onedimensional problem of a boundary layer formed at a constrained interface. Słowa kluczowe: gradient plasticity, geometrically necessary dislocations, boundary layer, size effects, indentation, finite element method Afiliacje autorów:
 25p.  
10.  Stupkiewicz S., Piccolroaz A.^{♦}, Bigoni D.^{♦}, Finitestrain formulation and FE implementation of a constitutive model for powder compaction, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2014.09.027, Vol.283, pp.856880, 2015 Streszczenie: A finitestrain formulation is developed, implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder. This constitutive model (as well as many others employed for geomaterials) embodies a number of features, such as pressuresensitive yielding, complex hardening rules and elastoplastic coupling, posing considerable problems in a finitestrain formulation and numerical implementation. A number of strategies are proposed to overcome the related problems, in particular, a neoHookean type of modification to the elastic potential and the adoption of the second Piola–Kirchhoff stress referred to the intermediate configuration to describe yielding. An incremental scheme compatible with the formulation for elastoplastic coupling at finite strain is also developed, and the corresponding constitutive update problem is solved by applying a return mapping algorithm. Słowa kluczowe: Plasticity, Elastoplastic coupling, Finite element method, Automatic differentiation Afiliacje autorów:
 45p.  
11.  Sadowski P., KowalczykGajewska K., Stupkiewicz S., Classical estimates of the effective thermoelastic properties of copper–graphene composites, COMPOSITES PART BENGINEERING, ISSN: 13598368, DOI: 10.1016/j.compositesb.2015.06.007, Vol.80, pp.278290, 2015 Streszczenie: Significant research effort is concentrated worldwide on development of graphenebased metalmatrix composites with enhanced thermomechanical properties. In this work, we apply two classical micromechanical meanfield theories to estimate the effective thermoelastic properties that can be achieved in practice for a copper–graphene composite. In the modelling, graphene is treated as an anisotropic material, and the effect of its outofplane properties, which are less recognized than the inplane properties, is studied in detail. To address the severe difficulties in processing of graphenebased metalmatrix composites, the copper–graphene composite is here assumed to additionally contain, due to imperfect processing, particles of graphite and voids. It is shown quantitatively that the related imperfections may significantly reduce the expected enhancement of the effective properties. The present predictions are also compared to the experimental data available in the literature. Słowa kluczowe: Metalmatrix composites (MMCs), Mechanical properties, Thermal properties, Micromechanics, Graphene Afiliacje autorów:
 40p.  
12.  KowalczykGajewska K., Sztwiertnia K.^{♦}, Kawałko J.^{♦}, Wierzbanowski K.^{♦}, Wroński M.^{♦}, Frydrych K., Stupkiewicz S., Petryk H., Texture evolution in titanium on complex deformation paths: Experiment and modelling, MATERIALS SCIENCE AND ENGINEERING ASTRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 09215093, DOI: 10.1016/j.msea.2015.04.040, Vol.637, pp.251263, 2015 Streszczenie: Texture evolution in commercially pure titanium deformed by equalchannel angular pressing (ECAP) and extrusion with forward–backward rotating die (KoBo) is studied both experimentally and numerically. New results are provided that demonstrate the effects of distinct and complex deformation paths on the texture in the ultrafine grained (UFG) material obtained after severe plastic deformation (SPD). The numerical simulations are based on the selfconsistent viscoplastic method of graintopolycrystal scale transition. A recently proposed modification of the probabilistic scheme for twinning is used that provides consistent values of the twin volume fraction in grains. The basic components of the experimentally observed texture are reasonably well reproduced in the modelling. The numerical simulations provide an insight into the internal mechanisms of plastic deformation, revealing substantial activity of mechanical twinning in addition to the basal and prismatic slip in titanium processed by ECAP. Słowa kluczowe: Texture evolution, UFG materials, SPD processes, Crystal plasticity, Twinning Afiliacje autorów:
 35p.  
13.  Stupkiewicz S., Piccolroaz A.^{♦}, Bigoni D.^{♦}, Elastoplastic coupling to model cold ceramic powder compaction, JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, ISSN: 09552219, DOI: 10.1016/j.jeurceramsoc.2013.11.017, Vol.34, pp.28392848, 2014 Streszczenie: The simulation of industrial processes involving cold compaction of powders allows for the optimization of the production of both traditional and advanced ceramics. The capabilities of a constitutive model previously proposed by the authors are explored to simulate simple forming processes, both in the small and in the large strain formulation. The model is based on the concept of elastoplastic coupling – providing a relation between density changes and variation of elastic properties – and has been tailored to describe the transition between a granular ceramic powder and a dense green body. Finite element simulations have been compared with experiments on an alumina readytopress powder and an aluminum silicate spraydried granulate. The simulations show that it is possible to take into account friction at the die wall and to predict the state of residual stress, density distribution and elastic properties in the green body at the end of the forming process. Słowa kluczowe: Ceramic forming, Granular material, Elastoplasticity, Constitutive model, Material modelling Afiliacje autorów:
 50p.  
14.  Stupkiewicz S., Denzer R.^{♦}, Piccolroaz A.^{♦}, Bigoni D.^{♦}, Implicit yield function formulation for granular and rocklike materials, COMPUTATIONAL MECHANICS, ISSN: 01787675, DOI: 10.1007/s0046601410478, Vol.54, pp.11631173, 2014 Streszczenie: The constitutive modelling of granular, porous and quasibrittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or ‘false elastic domains’) preventing the use of efficient returnmapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a returnmapping integration scheme is implemented and tested for elastic–plastic (or damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately. Słowa kluczowe: Plasticity, Return mapping algorithm, Automatic differentiation Afiliacje autorów:
 40p.  
15.  Korelc J.^{♦}, Stupkiewicz S., Closedform matrix exponential and its application in finitestrain plasticity, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.4653, Vol.98, pp.960987, 2014 Streszczenie: A new method to compute numerically efficient closedform representation of matrix exponential and its derivative is developed for 3 × 3 matrices with real eigenvalues. The matrix exponential is obtained by automatic differentiation of an appropriate scalar generating function in a general case, and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits illconditioning, for instance, for almost equal eigenvalues. Accuracy and numerical efficiency of the closedform matrix exponential as compared with the truncated series approximation are studied. The application of the closedform matrix exponential in the finitestrain elastoplasticity is also presented. To this end, several timediscrete evolution laws employing the exponential map are discussed for J2 plasticity with isotropic hardening and nonlinear kinematic hardening of Armstrong–Frederick type. The discussion is restricted to the case of elastic isotropy and implicit time integration schemes. In this part, the focus is on a general automatic differentiationbased formulation of finitestrain plasticity models. Numerical efficiency of the corresponding incremental schemes is studied in the context of the FEM. Słowa kluczowe: automatic differentiation, symbolic methods, ADB form, exponential map, kinematic hardening Afiliacje autorów:
 40p.  
16.  Kucharski S., Stupkiewicz S., Petryk H., Surface PileUp Patterns in Indentation Testing of Cu Single Crystals, EXPERIMENTAL MECHANICS, ISSN: 00144851, DOI: 10.1007/s1134001498831, Vol.54, pp.957969, 2014 Streszczenie: Nano and microindentation of Cu single crystals is performed in directions not aligned with crystallographic axes. Such tests correspond to mechanical characterization of incidentally oriented grains in a polycrystalline or composite material. Orientation and size dependence of complex patterns of surface pilingup and sinkingin around the imprint are investigated. Experimental observations are compared with finite element simulations based on the large deformation crystal plasticity theory. Słowa kluczowe: Copper, Nanoindentation, AFM, EBSD, Crystal plasticity, Finite element method Afiliacje autorów:
 35p.  
17.  Gourgiotis P.A.^{♦}, Stupkiewicz S., Macroscopic stress and strain in a doubly periodic array of dislocation dipoles, PROCEEDINGS OF THE ROYAL SOCIETY AMATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN: 13645021, DOI: 10.1098/rspa.2014.0309, Vol.470, pp.20140309116, 2014 Streszczenie: It is known that in twodimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the longrange character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem. Słowa kluczowe: dislocation dynamics, conditional convergence, micromechanics, Eshelby’s inclusion problem Afiliacje autorów:
 35p.  
18.  Stupkiewicz S., Lewandowski M.J., Lengiewicz J., Micromechanical analysis of friction anisotropy in rough elastic contacts, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/j.ijsolstr.2014.07.013, Vol.51, No.2324, pp.39313943, 2014 Streszczenie: Computational contact homogenization approach is applied to study friction anisotropy resulting from asperity interaction in elastic contacts. Contact of rough surfaces with anisotropic roughness is considered with asperity contact at the micro scale being governed by the isotropic Coulomb friction model. Application of a microtomacro scale transition scheme yields a macroscopic friction model with orientation and pressuredependent macroscopic friction coefficient. The macroscopic slip rule is found to exhibit a weak nonassociativity in the tangential plane, although the slip rule at the microscale is associated in the tangential plane. Counterintuitive effects are observed for compressible materials, in particular, for auxetic materials. Słowa kluczowe: Contact, Friction, Anisotropy, Roughness, Micromechanics Afiliacje autorów:
 35p.  
19.  Lengiewicz J., Wichrowski M.^{♦}, Stupkiewicz S., Mixed formulation and finite element treatment of the massconserving cavitation model, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2013.12.012, Vol.72, pp.143155, 2014 Streszczenie: A mixed formulation of the massconserving cavitation model is developed. The cavitation problem is formulated in terms of the hydrodynamic pressure and a complementary variable representing the void fraction in the cavitation zone. Weak form of the massbalance equation is consistently derived, and it exhibits subtle differences with respect to the available formulations. Finite element treatment preserves the twofield formulation, and a semismooth Newton method is applied to solve the resulting discretized equations. A monolithic Newtonbased scheme is also applied to solve the fully coupled elastohydrodynamic lubrication problem in the softEHL regime. Numerical examples illustrate the performance of the computational scheme. Słowa kluczowe: Lubrication, Cavitation, Reynolds equation, SoftEHL problem Afiliacje autorów:
 35p.  
20.  Zhao Y.^{♦}, Chen X.^{♦}, Park C.^{♦}, Fay C.C.^{♦}, Stupkiewicz S., Ke C.^{♦}, Mechanical deformations of boron nitride nanotubes in crossed junctions, JOURNAL OF APPLIED PHYSICS, ISSN: 00218979, DOI: 10.1063/1.4872238, Vol.115, pp.16430519, 2014 Streszczenie: We present a study of the mechanical deformations of boron nitride nanotubes (BNNTs) in crossed junctions. The structure and deformation of the crossed tubes in the junction are characterized by using atomic force microscopy. Our results show that the total tube heights are reduced by 20%–33% at the crossed junctions formed by doublewalled BNNTs with outer diameters in the range of 2.21–4.67 nm. The measured tube height reduction is found to be in a nearly linear relationship with the summation of the outer diameters of the two tubes forming the junction. The contact force between the two tubes in the junction is estimated based on contact mechanics theories and found to be within the range of 4.2–7.6 nN. The Young's modulus of BNNTs and their binding strengths with the substrate are quantified, based on the deformation profile of the upper tube in the junction, and are found to be 1.07 ± 0.11 TPa and 0.18–0.29 nJ/m, respectively. Finally, we perform finite element simulations on the mechanical deformations of the crossed BNNT junctions. The numerical simulation results are consistent with both the experimental measurements and the analytical analysis. The results reported in this paper contribute to a better understanding of the structural and mechanical properties of BNNTs and to the pursuit of their applications. Słowa kluczowe: Atomic force microscopy, Elastic moduli, Nanotubes, Carbon nanotubes, Finite element methods Afiliacje autorów:
 30p.  
21.  Stupkiewicz S., An ALE formulation for implicit time integration of quasisteadystate wear problems, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2013.03.023, Vol.260, pp.130142, 2013 Streszczenie: A fully coupled implicit scheme is developed for quasisteadystate wear problems. The formulation admits finite configuration changes due to both deformation and wear. The unconditionally stable implicit backwardEuler scheme is used for time integration of the shape evolution problem. Thus, the solution may proceed with large time increments, contrary to the commonly used explicit forwardEuler scheme, in which the time increment is restricted by the stability condition. This comes at the cost that the shape transformation mapping constitutes an additional unknown. As a result, a kind of an arbitrary Lagrangian–Eulerian (ALE) formulation is obtained in which the problem is solved simultaneously for the nodal positions and displacements. The incremental coupled problem is solved using the Newton method which leads to a highly efficient computational scheme, as illustrated by two and threedimensional numerical examples. Słowa kluczowe: Contact, Wear, Shape evolution, Arbitrary Lagrangian–Eulerian formulation, Automatic differentiation Afiliacje autorów:
 45p.  
22.  Stupkiewicz S., Petryk H., A robust model of pseudoelasticity in shape memory alloys, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.4405, Vol.93, No.7, pp.747769, 2013 Streszczenie: A model of pseudoelasticity in shape memory alloys is developed within the incremental energy minimization framework. Three constitutive functions are involved: the Helmholtz free energy and rateindependent dissipation that enter incrementally the minimized energy function, and the constraint function that defines the limit transformation strains. The proposed implementation is based on a unified augmented Lagrangian treatment of both the constitutive constraints and nonsmooth dissipation function. A methodology for easy reformulation of the model from the smallstrain to finitedeformation regime is presented. Finite element computations demonstrate robustness of the finitestrain version of the model and illustrate the effects of tension–compression asymmetry and transversal isotropy of the surface of limit transformation strains. Słowa kluczowe: shape memory alloys (SMA), phase transformation, energy methods, finite element method, augmented Lagrangian method Afiliacje autorów:
 40p.  
23.  Lengiewicz J., Stupkiewicz S., Efficient model of evolution of wear in quasisteadystate sliding contacts, WEAR, ISSN: 00431648, DOI: 10.1016/j.wear.2013.03.051, Vol.303, pp.611621, 2013 Streszczenie: A computationally efficient model of evolution of contact and wear is developed for a general periodic pinonflat problem with the focus on the pinondisc configuration and Archard wear model. The evolving contact state is assumed to be fully controlled by the wear process except during a short initial transient period controlled by both wear and elasticity. The contact pressure distribution is thus obtained by considering only the local wear model and the geometry of the conforming contact, without referring to the underlying elasticity problem. Evolution of the contact state is then obtained by time integration of the resulting rateproblem, and two computational schemes are developed for that purpose employing either the forward or the backwardEuler method. The model is successfully verified against a threedimensional finite element model. A dimensionless wearmode index specifying the relative magnitude of wear coefficients of the contact pair is introduced, and model predictions are presented as a function of this parameter. Słowa kluczowe: Contact mechanics, Wear, Simulation, Quasisteadystate process, Rigidwear model, Pinondisc Afiliacje autorów:
 35p.  
24.  KowalczykGajewska K., Stupkiewicz S., Modelling of Texture Evolution in Kobo Extrusion Process, ARCHIVES OF METALLURGY AND MATERIALS, ISSN: 17333490, DOI: 10.2478/v101720120160y, Vol.58, No.1, pp.113118, 2013 Streszczenie: The paper is aimed at modelling of evolution of crystallographic texture in KOBO extrusion which is an unconventional process of extrusion assisted by cyclic torsion. The analysis comprises two steps. In the first step, the kinematics of the KOBO extrusion process is determined using the finite element method. A simplifying assumption is adopted that the material flow is not significantly affected by plastic hardening, and thus a rigidviscoplastic material model with no hardening is used. In the second step, evolution of crystallographic texture is modelled along the trajectories obtained in the first step. A micromechanical model of texture evolution is used that combines the crystal plasticity model with a selfconsistent graintopolycrystal scale transition scheme, and the VPSC code is used for that purpose. Since each trajectory corresponds to a different deformation path, the resulting pole figures depend on the position along the radius of the extruded rod. Słowa kluczowe: plasticity, microstructure, crystallographic texture, KOBO extrusion Afiliacje autorów:
 20p.  
25.  Lengiewicz J., Stupkiewicz S., Continuum framework for finite element modelling of finite wear, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2010.12.020, Vol.205208, pp.178188, 2012 Streszczenie: A finite deformation contact problem with friction and wear is studied in which the shape changes due to wear are finite. Accordingly, in addition to the initial configuration and the current configuration, an intermediate timedependent configuration is introduced that corresponds to the undeformed body of the shape changed due to wear. Two time scales are also introduced in order to distinguish the fast time of the actual deformation (contact) problem from the slow time of the wear process (shape evolution problem). Separation of these time scales allows us to partially decouple the deformation problem and the shape evolution problem. Shape parameterization is introduced and the corresponding shape update scheme is formulated as a minimization problem. In particular, a secondorder scheme is developed which exploits shape sensitivities of the deformation problem. Numerical examples are provided to illustrate the performance and accuracy of the proposed numerical schemes. Słowa kluczowe: Frictional contact, Wear, Sensitivity analysis Afiliacje autorów:
 40p.  
26.  Petryk H., Stupkiewicz S., Instability of equilibrium of evolving laminates in pseudoelastic solids, INTERNATIONAL JOURNAL OF NONLINEAR MECHANICS, ISSN: 00207462, DOI: 10.1016/j.ijnonlinmec.2011.07.005, Vol.47, pp.317330, 2012 Streszczenie: This study is concerned with isothermal stability of equilibrium of evolving laminated microstructures in pseudoelastic solids with a multiwell free energy function. Several possible modes of instability associated with phase transition between energy wells are analysed. The related rateindependent dissipation is included by imposing a threshold value on the thermodynamic driving force. For a homogenized phasetransforming laminate with no length scale it is shown that localization instability is a rule in case of a nonzero interfacial jump of a directional nominal stress, irrespectively of actual boundary conditions. A stabilizing effect of elastic microstrain energy at the boundary of the localization zone is demonstrated for laminates of finite spacing. Illustrative numerical examples are given for an evolving austenite–martensite laminate in a crystal of CuZnAl shape memory alloy. Słowa kluczowe: Microstructures, Phase transformation, Laminates, Energy methods, Stability Afiliacje autorów:
 35p.  
27.  Petryk H., Stupkiewicz S., Modelling of microstructural evolution on complex paths of large plastic deformation, INTERNATIONAL JOURNAL OF MATERIALS RESEARCH, ISSN: 18625282, DOI: 10.3139/146.110683, Vol.103, No.3, pp.271277, 2012 Streszczenie: A procedure for the modelling of microstructural changes induced by nonuniform large plastic deformation of metals is developed. For a given plastic working process, a set of deformation paths for different initial locations of a material element is generated first for a nonhardening material by using the finite element method. Next, changes of a cellular microstructure and related hardening effects along each path are calculated by using a recently proposed model. The procedure is applied to a nonconventional process of cold extrusion assisted by cyclic rotation of the die. The evolution of microstructural parameters, their effect on strain hardening and a distribution map over the specimen crosssection are calculated. Słowa kluczowe: nonuniform deformation, dislocation cells, grain refinement, hardening, quantitative prediction Afiliacje autorów:
 30p.  
28.  Stupkiewicz S., Maciejewski G., Petryk H., Elastic microstrain energy of austenite–martensite interface in NiTi, MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING, ISSN: 09650393, DOI: 10.1088/09650393/20/3/035001, Vol.20, pp.0350019, 2012 Streszczenie: The interfacial energy due to elastic microstrains at the austenite–twinned martensite interface is calculated for the NiTi shape memory alloy undergoing cubictomonoclinic B2 ↔ B19' transformation. For each crystallographically distinct microstructure, an energetically favourable local shape of the interface is determined. The approach employs finite element computations and energy minimization with respect to shape parameters, taking into account elastic anisotropy of the phases and finitestrain kinematics. The effect of atomicscale interfacial energy is studied. Słowa kluczowe: microstructure, martensitic phase transformation, shape memory alloys (SMA), interface structure, micromechanical modelling Afiliacje autorów:
 30p.  
29.  Stupkiewicz S., GórzyńskaLengiewicz A., Almost compatible Xmicrostructures in CuAlNi shape memory alloy, CONTINUUM MECHANICS AND THERMODYNAMICS, ISSN: 09351175, DOI: 10.1007/s0016101102229, Vol.24, pp.149164, 2012 Streszczenie: A systematic study of a specific martensitic microstructure, called the Xmicrostructure, is carried out with the focus on the CuAlNi shape memory alloy undergoing the cubictoorthorhombic transformation. The set of all crystallographically distinct candidate Xmicrostructures is determined, and it is shown that, according to the crystallographic theory of martensite, none of them is compatible. Almost compatible Xmicrostructures, which involve elastic strains, are thus examined. These microstructures are searched in the neighborhood of all candidate Xmicrostructures by minimizing the total elastic strain energy with respect to the microstructure parameters. Several lowenergy Xmicrostructures are found, and it is shown that the total elastic strain energy correlates reasonably well with one of the indicators which characterize incompatibility of the corresponding candidate Xmicrostructure. Słowa kluczowe: Microstructure, Martensitic phase transformation, Shape memory alloys (SMA), Energy minimization Afiliacje autorów:
 20p.  
30.  Lengiewicz J., Korelc J.^{♦}, Stupkiewicz S., Automation of finite element formulations for large deformation contact problems, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.3009, Vol.85, pp.12521279, 2011 Streszczenie: The aim of this paper is to present a general method for automation of finite element formulations of large deformation contact problems. A new automaticdifferentiationbased notation is introduced that represents a bridge between the classical mathematical notation of contact mechanics and the actual computer implementation of contact finite elements. Automation of derivation of the required formulas (e.g. element residual and tangent matrix) combined with automatic code generation makes the finite element implementation possible at a moderate effort. Accordingly, several 3D contact formulations have been implemented in this work, including penalty and augmented Lagrangian treatments of contact constraints, and several contact smoothing techniques. A typical benchmark problem could thus be executed in an objective way leading to a comprehensive study of the efficiency and the accuracy of various formulations of 3D contact finite elements. Słowa kluczowe: automatic differentiation, symbolic methods, automation, frictional contact, contact smoothing, augmented Lagrangian method Afiliacje autorów:
 40p.  
31.  Stupkiewicz S., Lengiewicz J., Korelc J.^{♦}, Sensitivity analysis for frictional contact problems in the augmented Lagrangian formulation, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2010.03.021, Vol.199, No.33  36, pp.21652176, 2010 Streszczenie: Direct differentiation method of sensitivity analysis is developed for frictional contact problems. As a result of the augmented Lagrangian treatment of contact constraints, the direct problem is solved simultaneously for the displacements and Lagrange multipliers using the Newton method. The main purpose of the paper is to show that this formulation of the augmented Lagrangian method is particularly suitable for sensitivity analysis because the direct differentiation method leads to a noniterative exact sensitivity problem to be solved at each time increment. The approach is applied to a general class of threedimensional frictional contact problems, and numerical examples are provided involving large deformations, multibody contact interactions, and contact smoothing techniques. Słowa kluczowe: Sensitivity analysis, Direct differentiation method, Frictional contact, Augmented Lagrangian method Afiliacje autorów:
 32p.  
32.  Stupkiewicz S., Petryk H., A bicrystal aggregate model of pseudoelastic behaviour of shapememory alloy polycrystals, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 00207403, DOI: 10.1016/j.ijmecsci.2009.09.012, Vol.52, pp.219228, 2010 Streszczenie: A multiscale model of stressinduced phase transformation and martensite variant reorientation in shape memory alloy (SMA) polycrystals is developed. It is proposed to include neighbouringgrain interaction in a simple manner by introducing an intermediate bicrystal level into the sequential averaging scheme for SMA. The constitutive relationships are defined by specifying the free energy and dissipation functions. At the level of a single grain, the rateindependent dissipation function is used that incorporates the dissipation due to forward and reverse austenitetomartensite transformation as well as reorientation of martensite variants. The global response of the model is simulated numerically by minimizing the total incremental energy supply. Specific examples are calculated for a NiTi polycrystal for proportional and nonproportional loading paths. Słowa kluczowe: Phase transformation, Dissipation, Microstructure, Multiscale model, Incremental energy minimization Afiliacje autorów:
 32p.  
33.  Petryk H., Stupkiewicz S., Interfacial energy and dissipation in martensitic phase transformations. Part I: Theory, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 00225096, DOI: 10.1016/j.jmps.2009.11.004, Vol.58, pp.390408, 2010 Streszczenie: This paper is a continuation of the Part I (H. Petryk, S. Stupkiewicz, Interfacial energy and dissipation in martensitic phase transformations. Part I: Theory. J. Mech. Phys. Solids, 2010, doi:10.1016/j.jmps.2009.11.003). A fully threedimensional model of an evolving martensitic microstructure is examined, taking into account size effects due to the interfacial energy and also dissipation related to annihilation of interfaces. The elastic microstrain energy at microstructured interfaces is determined with the help of finite element computations and is approximated analytically. Three interface levels are examined: of grain boundaries attained by parallel martensite plates, of interfaces between austenite and twinned martensite, and of twin interfaces within the martensite phase. Minimization of the incremental energy supply, being the sum of the increments in the free energy and dissipation of the bulk and interfacial type at all levels, is used as the evolution rule, based on the theory presented in Part I. An example of the formation and evolution of a rankthree laminated microstructure of finite characteristic dimensions in a pseudoelastic CuAlNi shape memory alloy is examined quantitatively. Słowa kluczowe: Microstructures, Phase transformation, Grain boundaries, Energy methods, Shape memory alloys (SMA) Afiliacje autorów:
 32p.  
34.  Petryk H., Stupkiewicz S., Maciejewski G., Interfacial energy and dissipation in martensitic phase transformations. Part II: Size effects in pseudoelasticity, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 00225096, DOI: 10.1016/j.jmps.2009.11.003, Vol.58, pp.373389, 2010 Streszczenie: A model of evolving martensitic microstructures is formulated that incorporates the interfacial energy and dissipation on three different scales corresponding to the grain boundaries attained by martensite plates, the interfaces between austenite and martensite plates, and the twin interfaces within martensite plates. Three different time scales are also considered in order to clarify the meaning of rateindependent dissipation related to instabilities at more refined temporal and spatial scales. On the slowest time scale, the process of deformation and martensitic phase transformation is investigated as being composed of segments of smooth quasistatic evolution separated by sudden jumps associated with creation or annihilation of interfaces. A general evolution rule is used in the form of minimization of the incremental energy supply to the whole compound thermodynamic system, including the rateindependent dissipation. Close relationship is shown between the evolution rule and the thermodynamic condition for stability of equilibrium, with no a priori assumption on convexity of the dissipation function. It is demonstrated that the extension of the minimum principle from the firstorder rates to small but finite increments requires a separate symmetry restriction imposed on the state derivative of the dissipation function. Formulae for the dissipation associated with annihilation of interfaces are proposed that exhibit limited pathindependence and satisfy that symmetry requirement. By exploiting the incremental energy minimization rule with the help of the transport theorems, local propagation conditions are derived for both planar and curved phase transformation fronts. The theory serves as a basis for the algorithm for calculation of the stressinduced evolution of martensitic microstructures along with their characteristic dimensions and related hysteresis loops in shape memory alloys; the examples are given in Part II of the paper. Słowa kluczowe: Microstructures, Phase transformation, Grain boundaries, Energy methods, Stability Afiliacje autorów:
 32p.  
35.  Sadowski P., Stupkiewicz S., Combined effect of friction and macroscopic deformation on asperity flattening, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2010.04.011, Vol.43, pp.17351741, 2010 Streszczenie: The combined effect of friction and macroscopic plastic deformation on asperity flattening is studied. Crushing of a periodic array of wedgelike asperities is formulated as a rigidviscoplastic periodic indentation problem with superimposed macroscopic deformation. A micromechanical framework is developed and the corresponding boundary value problem is solved using the finite element method. An anomalous regime of asperity flattening is predicted at low flattening rates, in which the effect of friction on asperity flattening is opposite to that observed in the absence of macroscopic deformation and also at high flattening rates. An incremental elastoplastic analysis confirms this finding. Słowa kluczowe: Asperity flattening, Real contact area, Surface layer, Metal forming Afiliacje autorów:
 32p.  
36.  Sadowski P., Stupkiewicz S., A model of thermal contact conductance at high real contact area fractions, WEAR, ISSN: 00431648, Vol.268, pp.7785, 2010 Streszczenie: Thermal contact conductance (TCC) is studied in the whole range of real contact area fractions between zero and unity. For this purpose, a twoscale model is developed in which the effective (macroscopic) TCC coefficient is obtained from the solution of the heat conduction problem at the scale of asperities. Additional thermal resistance at the real contact spots is included in the model. The model is applied for several real 3D roughness topographies for which the effective TCC coefficient is determined as a function of the real contact area fraction and the local TCC coefficient at real contact spots. An analytical function is found which approximates this relationship in the whole range of parameters, and a characteristic lengthscale parameter is introduced which characterizes the effective TCC properties of a rough surface. Słowa kluczowe: Roughness topography, Real contact area, Thermal contact conductance, Characteristic length Afiliacje autorów:
 32p.  
37.  Stupkiewicz S., Petryk H., Grainsize effect in micromechanical modelling of hysteresis in shape memory alloys, ZAMMZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 00442267, DOI: 10.1002/zamm.201000008, Vol.90, pp.783795, 2010 Streszczenie: Size effects in pseudoelastic polycrystalline shape memory alloys are studied by considering a representative spherical laminated domain (subgrain) and its interfacial energy at three scales: at the subgrain boundaries, at the austenite–martensite interfaces, and at the twin boundaries. Two sources of interfacial energy are accounted for, namely the atomicscale energy of twin and phase boundaries and the elastic strain energy at microstructured interfaces, the latter being predicted theoretically. The evolution of microstructure of the representative domain is determined using the incremental energy minimization rule applied to the sum of the increments in the Helmholtz free energy and rateindependent dissipation. The sizedependent part of dissipation is estimated by assuming that negative increments in interfacial energy, associated with annihilation of interfaces, cannot be reverted back into the bulk free energy and are thus dissipated. Simple analytic formula for the interfacial energy dissipated in a complete forwardreverse transformation cycle is derived and combined with a micromechanical model of a polycrystalline NiTi shape memory alloy. A numerical example illustrating sizedependent hysteresis in the stressinduced martensitic transformation is presented. Słowa kluczowe: interfacial energy, incremental energy minimization, dissipation, martensitic transformation Afiliacje autorów:
 20p.  
38.  Petryk H., Stupkiewicz S., Energia powierzchniowa, dyssypacja i efekty skali w modelowaniu mikrostruktur martenzytycznych, Czasopismo Techniczne. Mechanika, ISSN: 00114561, Vol.107, No.20, pp.99108, 2010 Streszczenie: W niniejszym artykule przedstawiono energetyczne podejście do wieloskalowego modelowania ewolucji mikrostruktur martenzytycznych w stopach z pamięcią kształtu. Energia swobodna Helmholtza i energia dyssypowana w układzie reprezentowane są przez sumy członów odpowiadających energii objętościowej oraz energii powierzchniowej na granicach mikrostrukturalnych pomiędzy poszczególnymi wariantami martenzytu, fazami lub ziarnami. Ewolucja mikrostruktury jest wyznaczana drogą przyrostowej minimalizacji całkowitej energii dostarczanej do rozpatrywanego układu w procesie makroskopowo quasistatycznym i izotermicznym. Ogólną procedurę zastosowano do numerycznych symulacji powstawania i ewolucji warstwowych struktur martenzytycznych indukowanych naprężeniowo w stopach z pamięcią kształtu. W energii powierzchniowej uwzględniono energię mikroodkształceń sprężystych w otoczeniu granic mikrostrukturalnych, wyznaczoną przy użyciu metody elementów skończonych. Policzone przykłady opisują ewolucję mikrostruktury martenzytycznej w formie laminatu trzeciego rzędu w stopie CuAlNi dla przemiany β1→γ1′ oraz jej zależność od sposobu uwzględnienia dyssypacji energii powierzchniowej. Słowa kluczowe: energia powierzchniowa, minimalizacja energii, przemiana martenzytyczna Afiliacje autorów:
 6p.  
39.  Stupkiewicz S., Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime, COMPUTATIONAL MECHANICS, ISSN: 01787675, DOI: 10.1007/s0046600903943, Vol.44, pp.605619, 2009 Streszczenie: Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacementbased FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higherorder interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an Oring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly. Słowa kluczowe: Contact, Elastohydrodynamic lubrication, Finite element method, Discontinuous Galerkin method, Elastomeric seal Afiliacje autorów:
 32p.  
40.  Stupkiewicz S., Marciniszyn A.^{♦}, Elastohydrodynamic lubrication and finite configuration changes in reciprocating elastomeric seals, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2008.08.008, Vol.42, pp.615627, 2009 Streszczenie: A computational framework has been developed for a fully coupled analysis of elastohydrodynamic lubrication and finite deformations of elastomeric reciprocating seals in hydraulic actuators. The relevant formulation is provided, which consistently treats finite configuration changes of the seal modelled as a hyperelastic (MooneyRivlin) solid. The steadystate hydrodynamic lubrication is modelled using the classical Reynolds equation. Coupling of the solid and fluid parts is fully accounted for, including friction due to shear stresses in the lubricant film. Detailed results of finite element simulations are provided for two benchmark problems of Oring and rectangular rod seals in a wide range of process parameters. Słowa kluczowe: Elastohydrodynamic lubrication, Hyperelastic model, Dynamic sealing Afiliacje autorów:
 32p.  
41.  Petryk H., Stupkiewicz S., Kuziak R.^{♦}, Grain refinement and strain hardening in IF steel during multiaxis compression: Experiment and modelling, JOURNAL OF MATERIALS PROCESSING TECHNOLOGY, ISSN: 09240136, DOI: 10.1016/j.jmatprotec.2007.11.068, Vol.204, pp.255263, 2008 Streszczenie: The effect of severe plastic deformation (SPD) during cyclic multiaxis compression on grain refinement and strain hardening in interstitial free (IF) steel is studied quantitatively. In the experimental part, the material samples were cold deformed in the MAXStrain(R) system by successive compression in two mutually orthogonal directions. The electron backscatter diffraction (EBSD) technique was used to measure the average spacing of the dislocation cell (low angle) and cellblock (high angle) boundaries. In the modelling part, the decrease in size of dislocation cells and cell blocks was expressed in terms of the effective plastic strain defined such that strainrate reversals slow down its accumulation. The strengthening effect of microstructural evolution was included in the continuum mechanics framework of finite strain plasticity. Examples of simulation of the behaviour of IF steel severely deformed by multiaxis compression are calculated and compared to experimental data. Słowa kluczowe: Modelling, Microstructure, Hardening, Severe plastic deformation Afiliacje autorów:
 
42.  Stupkiewicz S., Maciejewski G., Petryk H., Lowenergy morphology of the interface layer between austenite and twinned martensite, ACTA MATERIALIA, ISSN: 13596454, DOI: 10.1016/j.actamat.2007.07.034, Vol.55, No.18, pp.62926306, 2007 Streszczenie: A micromechanical scheme is developed for predicting the morphology and interfacial energy of the interface layer between the parent phase and internally twinned martensite. Lowenergy morphologies are determined by minimizing, with respect to shape parameters, the elastic microstrain energy associated with local incompatibility of transformation strains. The computational scheme involves a finite element solution to a problem of nonlinear elasticity with eigenstrains, shape sensitivity analysis with respect to general shape parametrization and minimization employing a gradientbased algorithm. As an application, lowenergy morphologies are studied for the austenite–martensite interface in the cubictoorthorhombic transformation in a CuAlNi shape memory alloy. Discussion of the results of the analysis includes comparison to alternative simplified methods in terms of the predicted morphologies and the corresponding interfacial energies. Słowa kluczowe: Microstructure, Martensitic phase transformation, Shape memory alloys (SMA), Interface structure, Micromechanical modelling Afiliacje autorów:
 
43.  Petryk H., Stupkiewicz S., A quantitative model of grain refinement and strain hardening during severe plastic deformation, MATERIALS SCIENCE AND ENGINEERING ASTRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 09215093, DOI: 10.1016/j.msea.2006.08.076, Vol.444, pp.214219, 2007 Streszczenie: The effect of severe plastic deformation (SPD) on grain refinement and strain hardening in polycrystalline metals is studied quantitatively. The decrease in size of dislocation cells and cellblocks is expressed as a function of the effective plastic strain influenced by strainrate reversals. The estimated growth of the highangle boundary area fraction depends on the complexity of the threedimensional deformation path. The strain hardening due to both dislocation and boundary strengthening is described in terms of microstructural parameters and incorporated in the continuum mechanics framework of finite strain plasticity. The proposed model provides a tool for quantitative comparison of different SPD processes. Examples of simulation of the behaviour of pure aluminium deformed by equal channel angular pressing (ECAP) and cyclic extrusion–compression are calculated. Słowa kluczowe: Modelling, Microstructure, Severe plastic deformation, Ultrafine grained materials Afiliacje autorów:
 
44.  Richert M.^{♦}, Petryk H., Stupkiewicz S., Grain refinement in AlMgSi alloy during cyclic extrusioncompression: Experiment and modelling, ARCHIVES OF METALLURGY AND MATERIALS, ISSN: 17333490, Vol.52, pp.4954, 2007 Streszczenie: The effect of severe plastic deformation (SPD) during cyclic extrusioncompression (CEC) on grain refinement and strain hardening in AlMgSi alloy is studied quantitatively. New experimental results are presented showing that the average microband thickness and grain size decrease below 100 nm, i.e. a nanocrystalline material is obtained. In the modelling part, the decrease in size of dislocation cells and microbands is expressed in terms of the effective plastic strain defined such that strain rate reversals slow down its accumulation. Examples of simulation of the behaviour of AlMgSi alloy severely deformed by cyclic extrusioncompression are calculated and compared to experimental data. Słowa kluczowe: Modelling, Microstructure, Hardening, Severe plastic deformation Afiliacje autorów:
 
45.  Stupkiewicz S., Petryk H., Finitestrain micromechanical model of stressinduced martensitic transformations in shape memory alloys, MATERIALS SCIENCE AND ENGINEERING ASTRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, ISSN: 09215093, DOI: 10.1016/j.msea.2006.01.112, Vol.438440, pp.126130, 2006 Streszczenie: A micromechanical model of stressinduced martensitic transformation in single crystals of shape memory alloys is developed. This model is a finitestrain counterpart to the approach presented recently in the smallstrain setting [S. Stupkiewicz, H. Petryk, J. Mech. Phys. Solids 50 (2002) 2303–2331]. The stressinduced transformation is assumed to proceed by the formation and growth of parallel martensite plates within the austenite matrix. Propagation of phase transformation fronts is governed by a rateindependent thermodynamic criterion with a threshold value for the thermodynamic driving force, including in this way the intrinsic dissipation due to phase transition. This criterion selects the initial microstructure at the onset of transformation and governs the evolution of the laminated microstructure at the macroscopic level. A multiplicative decomposition of the deformation gradient into elastic and transformation parts is assumed, with full account for the elastic anisotropy of the phases. The pseudoelastic behavior of Cu–Zn–Al single crystal in tension and compression is studied as an application of the model. Słowa kluczowe: Microstructures, Laminates, Finite deformations, Micromechanics, Shape memory alloys Afiliacje autorów:
 
46.  Maciejewski G., Stupkiewicz S., Petryk H., Elastic microstrain energy at the austenitetwinned martensite interface, ARCHIVES OF MECHANICS, ISSN: 03732029, Vol.57, No.4, pp.277297, 2005 Streszczenie: A micromechanical scheme is developed for the analysis of elastic microstrains induced by local incompatibilities at the austenitetwinned martensite interface. The aim of the paper is to estimate the elastic microstrain energy which is an important factor in the formation of microstructures during the martensitic transformation. The finite deformation framework is applied, consistent with the crystallographic theory of martensite, and full account is taken for elastic anisotropy of the phases. As an example, the microstructures in the cubictoorthorhombic transformation in CuAlNi shape memory alloy are analyzed by the finite element method for the assumed class of zigzag shapes of the austenitemartensite interface at the microlevel. Finally, the effect of the interphase boundary energy on the microstructure of the transition layer is studied. Słowa kluczowe: microstructure, martensitic phase transformation, shape memory alloys (SMA), interface structure, micromechanical modelling Afiliacje autorów:
 
47.  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:
 
48.  Stupkiewicz S., Petryk H., Modelling of laminated microstructures in stressinduced martensitic transformations, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 00225096, DOI: 10.1016/S00225096(02)000297, Vol.50, No.11, pp.23032331, 2002 Streszczenie: This paper is concerned with micromechanical modelling of stressinduced martensitic transformations in crystalline solids, with the focus on distinct elastic anisotropy of the phases and the associated redistribution of internal stresses. Micro–macro transition in stresses and strains is analysed for a laminated microstructure of austenite and martensite phases. Propagation of a phase transformation front is governed by a timeindependent thermodynamic criterion. Plasticitylike macroscopic constitutive rate equations are derived in which the transformed volume fraction is incrementally related to the overall strain or stress. As an application, numerical simulations are performed for cubic β1 (austenite) to orthorhombic γ1′ (martensite) phase transformation in a single crystal of Cu–Al–Ni shape memory alloy. The pseudoelasticity effect in tension and compression is investigated along with the corresponding evolution of internal stresses and microstructure. Słowa kluczowe: Phase transformation, Microstructures, Layered material, Constitutive behaviour, Shape memory alloy Afiliacje autorów:
 
49.  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:
 
50.  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:
 
51.  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:
 
52.  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:
 
53.  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:

Lista ostatnich monografii
1. 71  Stupkiewicz S., Micromechanics of contact and interphase layers, Lecture Notes in Applied and Computational Mechanics, Springer, 30, pp.1196, 2007 
2. 72  Stupkiewicz S., Micromechanics of contact and interphase layers, Rozprawa habilitacyjna, IPPT Reports on Fundamental Technological Research, 2, pp.1244, 2005 
Lista rozdziałów w ostatnich monografiach
1. 16  Gambin B., Lekszycki T., Kowalczyk T., Kowalewski T.A., Ziółkowski A., Pieczyska E.A., Stupkiewicz S., Scenariusze rozwoju technologii nowoczesnych materiałów metalicznych, ceramicznych i kompozytowych, rozdział: Biomateriały. Rola i strategia badawcza IPPT PAN w powstaniu nowoczesnych technologii materiałów współpracujących z ludzkimi tkankami, Wydawnictwo Naukowe Instytutu Technologii Eksploatacji PIB, 1, pp.181222, 2010 
2. 212  Petryk H., Stupkiewicz S., Workshop in Memory of Prof. J.R. Klepaczko: Dynamic Behaviour of Materials, rozdział: Modelling of strain hardening and grain refinement during severe plastic deformation, LPMM, Metz, Rusinek A., Chevrier P. (Eds.), pp.4350, 2009 
3. 131  Korelc J.^{♦}, Lengiewicz J., Stupkiewicz S., Analysis and simulation of contact problems, Lecture notes in applied and computational mechanics, rozdział: A study of symbolic description, numerical efficiency and accuracy of 2D and 3D contact formulations, Springer, Wriggers P., Nackenhorst U. (Eds.), 27, pp.111118, 2006 
4. 132  Lengiewicz J., Stupkiewicz S., Korelc J.^{♦}, Rodic T.^{♦}, Analysis and simulation of contact problems, Lecture notes in applied and computational mechanics, rozdział: DDMbased sensitivity analysis and optimization for smooth contact formulations, Springer, Wriggers P., Nackenhorst U. (Eds.), 27, pp.7986, 2006 
5. 133  Stupkiewicz S., Sadowski P., Analysis and simulation of contact problems, Lecture notes in applied and computational mechanics, rozdział: Micromechanical analysis of deformation and temperature inhomogeneities within rough contact layers, Springer, Wriggers P., Nackenhorst U. (Eds.), 27, pp.325332, 2006 
6. 159  Petryk H., Stupkiewicz S., Maciejewski G., IUTAM Symposium on size effects on material and structural behaviour at micron and nanoscales, rozdział: Modelling of austenite/martensite laminates with interfacial energy effect, Springer, Tong P., Sun Q.P. (Eds.), pp.151162, 2006 
7. 182  Petryk H., Stupkiewicz S., Maciejewski G., Proceedings IUTAM Symp. on Size Effects on Material and Structural Behaviour at Micron and Nanoscales, rozdział: Modeling of austenite/martensite laminates with interfacial energy effect, Springer, pp.151162, 2006 
8. 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 
9. 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 
10. 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 
Prace konferencyjne
1.  KowalczykGajewska K., Stupkiewicz S., Frydrych K., Petryk H., Modelling of Texture Evolution and Grain Refinement on Complex SPD Paths, JOURNAL OF PHYSICS: CONFERENCE SERIES, ISSN: 17426588, DOI: 10.1088/1757899X/63/1/012040, No.63, pp.012040110, 2014 Streszczenie: A computationally efficient procedure for modelling of microstructural changes on complex and spatially nonuniform deformation paths of severe plastic deformation (SPD) is presented. The analysis follows a twostep procedure. In the first step, motivated by saturation of material hardening at large accumulated strains, the steadystate kinematics of the process is generated for a nonhardening viscoplastic model by using the standard finite element method for a specified SPD scheme. In the second step, microstructural changes are investigated along the deformationgradient trajectories determined in the first step for different initial locations of a material element. The aim of this study is to predict texture evolution and grain refinement in a nonconventional process of cold extrusion assisted by cyclic rotation of the die, called KOBO process, which leads to an ultrafine grain structure. The texture evolution is calculated for fcc and hcp metals by applying crystal viscoplasticity combined with the selfconsistent scale transition scheme. In parallel, by applying the simplified phenomenological model of microstructure evolution along the trajectories, grain refinement is modelled. The results are compared with available experimental data. Słowa kluczowe: SPD processes, Texture evolution, UFG materials, Crystal plasticity, Grain refinement Afiliacje autorów:
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Abstrakty konferencyjne
1.  Sadowski P., KowalczykGajewska K., Stupkiewicz S., Micromechanical modelling of elastoplastic composites: efficient and robust finiteelement implementation of MoriTanaka model, CNM, 5th Conference on Nano and Micromechanics, 20170704/0706, Wrocław (PL), No.O08, pp.3133, 2017 Słowa kluczowe: Meanfield homogenization, MoriTanaka method, Composite materials, Finite element method Afiliacje autorów:
 
2.  Tůma K., Stupkiewicz S., Petryk H., The effect of twin spacing on the morphology of austenitetwinned martensite interface, SolMech 2016, 40th Solid Mechanics Conference, 20160829/0902, Warszawa (PL), No.P069, pp.1, 2016  
3.  Sadowski P., KowalczykGajewska K., Stupkiewicz S., Efficient algorithmic treatment of the incremental Mori–Tanaka scheme for elastoplastic composites, SolMech 2016, 40th Solid Mechanics Conference, 20160829/0902, Warszawa (PL), No.P070, pp.12, 2016  
4.  Tůma K., Stupkiewicz S., Petryk H., Phasefield modelling of twinning and martensitic transformation at finite strain, PCMCMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 20150908/0911, Gdańsk (PL), pp.815816, 2015 Streszczenie: We develop a micromechanical phasefield model that describes the transformation between the austenite and twinned martensites. The new model constrains the volume fractions of both parent and internally twinned phases such that the physically motivated bounds are not violated. As an application, we studied the twinned martensite and austenitemartensite interfaces in the cubictoorthorhombic transformation in a CuAlNi shape memory alloy and estimated the elastic part of the interfacial energy. Afiliacje autorów:
 
5.  Lengiewicz J., Sadowski P., Stupkiewicz S., Finite element modelling of elastohydrodynamic lubrication in the finite deformation regime, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.4344, 2014  
6.  Sadowski P., Stupkiewicz S., Estimation of the effective properties of composites with inclusions of diverse shapes and properties, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.139140, 2014  
7.  Frydrych K., KowalczykGajewska K., Stupkiewicz S., Modelling of microstructure evolution in hcp polycrystals on nonproportional strain paths, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.207208, 2014 Streszczenie: Microstructure evolution in hcp polycrystals subjected to severe plastic deformation, in particular in the KOBO extrusion and the equal channel angular pressing (ECAP) processes, are examined in this work, using the crystal plasticity framework. Modelling approach combines the large strain crystal plasticity model accounting for twinning and the tangent variant of the selfconsistent (SC) scale transition scheme. Słowa kluczowe: hcp polycrystals, twinning, SPD processes, crystal plasticity, selfconsistent model, microstructure evolution Afiliacje autorów:
 
8.  Sadowski P., Kucharski S., Lengiewicz J., Stupkiewicz S., Soft elastohydrodynamic lubrication problems in the finite deformation regime: experimental testing and modelling, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.323324, 2014 