Homogenisation of structured elastoviscoplastic solids

An irregularly structured solid A tensile test on a polycarbonate plate with irregularly distributed rubber inclusions is simulated in two different ways: (1) a homogeneous simulation using homogenised material parameters from the irregular unit cell (CPU-time: 3 hours); (2) a heterogeneous simulation where the structure is completely discretised (‘reference solution’: CPU-time: 4 days): specimen

[1]  Fe Frans Veldpaus,et al.  On the implementation of finite strain plasticity equations in a numerical model , 1984 .

[2]  P. Chadwick.  Continuum Mechanics: Concise Theory and Problems , 1976 .

[3]  W. Brekelmans,et al.  Prediction of the large-strain mechanical response of heterogeneous polymer systems : local and global deformation behaviour of a representative volume element of voided polycarbonate , 1999 .

[4]  L. J. Sluys,et al.  Interaction between material length scale and imperfection size for localisation phenomena in viscoplastic media , 1996 .

[5]  O. C. Zienkiewicz,et al.  The finite element method, fourth edition; volume 2: solid and fluid mechanics, dynamics and non-linearity , 1991 .

[6]  A. Needleman,et al.  A tangent modulus method for rate dependent solids , 1984 .

[7]  E. Stein,et al.  Finite-Element Simulation of Elastoplastic Properties of Two-Phase Composites Reinforced by Particles , 1996 .

[8]  D. Owen,et al.  A Model for Large Deformations of Elasto-Viscoplastic Solids at Finite Strain: Computational Issues , 1992 .

[9]  R. Toupin.  Elastic materials with couple-stresses , 1962 .

[10]  P. Perzyna.  Thermodynamic Theory of Viscoplasticity , 1971 .

[11]  L. B. Freund,et al.  Deformation trapping due to thermoplastic instability in one-dimensional wave propagation , 1984 .

[12]  Ugo Galvanetto,et al.  NUMERICAL HOMOGENIZATION OF PERIODIC COMPOSITE MATERIALS WITH NON-LINEAR MATERIAL COMPONENTS , 1999 .

[13]  A. Needleman.  Material rate dependence and mesh sensitivity in localization problems , 1988 .

[14]  W. Brekelmans,et al.  Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling , 2000 .

[15]  Fpt Frank Baaijens,et al.  An approach to micro-macro modeling of heterogeneous materials , 2001 .

[16]  P. M. Squet.  Local and Global Aspects in the Mathematical Theory of Plasticity , 1985 .

[17]  J. Z. Zhu,et al.  The finite element method , 1977 .

[18]  A. Anthoine.  Derivation of the in-plane elastic characteristics of masonry through homogenization theory , 1995 .

[19]  J. Brockenbrough,et al.  A Three-Dimensional Unit Cell Model With Application Toward Particulate Composites , 1995 .

[20]  Ta Theo Tervoort,et al.  Constitutive modelling of polymer glasses : finite, nonlinear viscoelastic behaviour of polycarbonate , 1996 .

[21]  G. Weng,et al.  A secant-viscosity approach to the time-dependent creep of an elastic viscoplastic composite , 1997 .

[22]  M. Boyce,et al.  Large inelastic deformation of glassy polymers. part I: rate dependent constitutive model , 1988 .

[23]  D. Borst,et al.  Fundamental issues in finite element analyses of localization of deformation , 1993 .

[24]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[25]  L. Anand,et al.  Finite deformation constitutive equations and a time integrated procedure for isotropic hyperelastic—viscoplastic solids , 1990 .

[26]  Wam Marcel Brekelmans,et al.  The Influence of Intrinsic Strain Softening on Strain Localization in Polycarbonate: Modeling and Experimental Validation , 2000 .

[27]  W. Nowacki,et al.  Theory of asymmetric elasticity , 1986 .

[28]  T. R. Hughes,et al.  Mathematical foundations of elasticity , 1982 .

[29]  V. Levitas.  Some Relations for Finite Inelastic Deformation of Microheterogeneous Materials with Moving Discontinuity Surfaces , 1996 .

[30]  W. Brekelmans,et al.  Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling , 1998 .

[31]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects , 1988 .

[32]  V. D. O. Sluis,et al.  Homogenisation of heterogeneous viscoplastic materials , 1999 .

[33]  R. Hill,et al.  On macroscopic effects of heterogeneity in elastoplastic media at finite strain , 1984, Mathematical Proceedings of the Cambridge Philosophical Society.

[34]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[35]  Sia Nemat-Nasser,et al.  Averaging theorems in finite deformation plasticity , 1999 .

[36]  Fpt Frank Baaijens.  Calculation of residual stresses in injection molded products , 1991 .

[37]  Djordje Peric,et al.  On a class of constitutive equations in viscoplasticity : formulation and computational issues , 1993 .

[38]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[39]  Akhtar S. Khan,et al.  Continuum theory of plasticity , 1995 .

[40]  S. Hazanov,et al.  Hill condition and overall properties of composites , 1998 .

[41]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[42]  J. Ju,et al.  Effective elastoplastic behavior of two-phase ductile matrix composites: A micromechanical framework , 1996 .

[43]  M. Li,et al.  Microstructural characterization, meso-scale modeling and multiple-scale analysis of discretely reinforced materials , 1998 .

[44]  Numerical Simulation of the Effective Elastic Properties of a Class of Cell Materials , 1998 .

[45]  A. I. Leonov.  Nonequilibrium thermodynamics and rheology of viscoelastic polymer media , 1976 .

[46]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[47]  S. Nemat-Nasser.  On finite deformation elasto-plasticity , 1982 .

[48]  Somnath Ghosh,et al.  A microstructure based numerical method for constitutive modeling of composite and porous materials , 1999 .

[49]  W. Brekelmans.  Nonlocal formulation of the evolution of damage in a one-dimensional configuration , 1993 .

[50]  J. C. Simo,et al.  Remarks on rate constitutive equations for finite deformation problems: computational implications , 1984 .

[51]  Wam Marcel Brekelmans,et al.  A Constitutive Equation for the Elasto-Viscoplastic Deformation of Glassy Polymers , 1997 .

[52]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[53]  V. Giessen,et al.  Void growth in glassy polymers , 1997 .

[54]  Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials , 1999 .

[55]  Djordje Peric,et al.  On consistent stress rates in solid mechanics: Computational implications , 1992 .

[56]  Somnath Ghosh,et al.  Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model , 1996 .

[57]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[58]  Fpt Frank Baaijens,et al.  HOMOGENIZATION OF THE ELASTOPLASTIC BEHAVIOR OF PERFORATED PLATES , 1998 .

[59]  Milos Kojic,et al.  Studies of finite element procedures—Stress solution of a closed elastic strain path with stretching and shearing using the updated Lagrangian Jaumann formulation , 1987 .

[60]  S. Timoshenko,et al.  Mechanics of Materials, 3rd Ed. , 1991 .

[61]  J. Schröder,et al.  Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials , 1999 .

[62]  T. Hughes.  Numerical Implementation of Constitutive Models: Rate-Independent Deviatoric Plasticity , 1984 .

[63]  Anne Hoger,et al.  The stress conjugate to logarithmic strain , 1987 .

[64]  P. Perzyna,et al.  Modified theory of viscoplasticity. Physical foundations and identification of material functions for advanced strains , 1983 .

[65]  R. Borst.  Simulation of localisation using Cosserat theory: a reappraisal of the Cosserat continuum. , 1991 .

[66]  Eduard Rohan,et al.  Shape optimization of elasto-plastic structures and continua , 2000 .

[67]  O. C. Zienkiewicz,et al.  Basic formulation and linear problems , 1989 .

[68]  Mary C. Boyce,et al.  Evolution of plastic anisotropy in amorphous polymers during finite straining , 1993 .

[69]  S. Torquato,et al.  Scale effects on the elastic behavior of periodic andhierarchical two-dimensional composites , 1999 .

[70]  Heh Han Meijer,et al.  Effective properties of a viscoplastic constitutive model obtained by homogenisation , 1999 .

[71]  Jacek Skrzypek,et al.  Plasticity and Creep Theory Examples and Problems , 1993 .

[72]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multipli , 1988 .

[73]  Kyung K. Choi,et al.  Design sensitivity analysis and shape optimization of structural components with hyperelastic material , 2000 .

[74]  Christian Huet,et al.  Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume , 1994 .

[75]  P. Perzyna.  Fundamental Problems in Viscoplasticity , 1966 .

[76]  Pedro Ponte Castañeda.  Exact second-order estimates for the effective mechanical properties of nonlinear composite materials , 1996 .

[77]  J. Chaboche,et al.  FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials , 2000 .

[78]  P. P. Timmermans,et al.  Evaluation of a constitutive model for solid polymeric materials : model selection and parameter quantification , 1997 .

[79]  Peidong Wu,et al.  Analysis of shear band propagation in amorphous glassy polymers , 1994 .

[80]  M. Ostoja-Starzewski.  Scale effects in materials with random distributions of needles and cracks , 1999 .

[81]  J. Nagtegaal,et al.  Some computational aspects of elastic-plastic large strain analysis , 1981 .

[82]  Christian Huet,et al.  Coupled size and boundary-condition effects in viscoelastic heterogeneous and composite bodies , 1999 .

[83]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[84]  G. Bao.  On Strain-Rate Sensitivity of Metal Matrices Reinforced with Ceramic Particles , 1996 .

[85]  M. B. Rubin,et al.  A time integration procedure for plastic deformation in elastic-viscoplastic metals , 1989 .

[86]  Nicolas Triantafyllidis,et al.  A gradient approach to localization of deformation. I. Hyperelastic materials , 1986 .

[87]  David J. Smith,et al.  Finite element micromechanical modelling of yield and collapse behaviour of metal matrix composites , 2000 .

[88]  Christian Huet,et al.  Application of variational concepts to size effects in elastic heterogeneous bodies , 1990 .

[89]  S. Nemat-Nasser,et al.  Rate-dependent, finite elasto-plastic deformation of polycrystals , 1986, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[90]  Kenjiro Terada,et al.  Nonlinear homogenization method for practical applications , 1995 .

[91]  R. de Borst,et al.  Wave propagation and localization in a rate-dependent cracked medium-model formulation and one-dimensional examples , 1992 .

[92]  Colby C. Swan,et al.  Techniques for stress- and strain-controlled homogenization of inelastic periodic composites , 1994 .

[93]  Zdenek P. Bazant,et al.  Why Continuum Damage is Nonlocal: Micromechanics Arguments , 1991 .

[94]  D. Owen,et al.  Finite elements in plasticity : theory and practice , 1980 .

[95]  Phj Pieter Vosbeek.  A micromechanical approach to deformation and failure of discrete media , 1994 .

[96]  Bruno Sudret,et al.  A two-phase elastoplastic model for unidirectionally-reinforced materials , 1999 .

[97]  P.J.G. Schreurs,et al.  Homogenization of heterogeneous polymers , 1999 .

[98]  李幼升,et al.  Ph , 1989 .

[99]  W. Drugan,et al.  A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites , 1996 .

[100]  Rjm Robert Smit.  Toughness of heterogeneous polymeric systems : a modeling approach , 1998 .

[101]  M. Amieur,et al.  Numerical and Experimental Assessment of the Size and Boundary Conditions Effects for the Overall Properties of Granular Composite Bodies Smaller than the Representative Volume , 1995 .

[102]  N. Kikuchi,et al.  Simulation of the multi-scale convergence in computational homogenization approaches , 2000 .

[103]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[104]  G. Maugin.  The Thermomechanics of Plasticity and Fracture , 1992 .

[105]  P. Suquet,et al.  Effective properties of porous ideally plastic or viscoplastic materials containing rigid particles , 1997 .

[106]  J. Pan,et al.  A macroscopic constitutive law for porous solids with pressure-sensitive matrices and its implications to plastic flow localization , 1995 .