Instability phenomena in plasticity: Modelling and computation

SummaryWe presented aspects and results related to the broad field of strain localization with special focus on large strain elastoplastic response. Therefore, we first re-examined issues related to the classification of discontinuities and the classical description of localization with a particular emphasis on an Eulerian geometric representation. We touched the problem of mesh objectivity and discussed results of a particular regularization method, namely the micropolar approach. Generally, regularization has to preserve ellipticity and to reflect the underlying physics. For example ductile materials have to be modelled including viscous effects whereas geomaterials are adequately described by the micropolar approach. Then we considered localization phenomena within solids undergoing large strain elastoplastic deformations. Here, we documented the influence of isotropic damage on the failure analysis. Next, the interesting influence of an orthotropic yield condition on the spatial orientation of localized zones has been studied. Finally, we investigated the localization condition for an algorithmic model of finite strain single crystal plasticity.

[1]  J. Lemaître.  How to use damage mechanics , 1984 .

[2]  Hans Muhlhaus,et al.  A variational principle for gradient plasticity , 1991 .

[3]  I. Vardoulakis,et al.  The thickness of shear bands in granular materials , 1987 .

[4]  A. Gurson.  Plastic flow and fracture behavior of ductile materials incorporating void nucleation, growth and interaction , 1988 .

[5]  J. C. Simo,et al.  Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory , 1992 .

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

[7]  Christian Miehe,et al.  Computation of isotropic tensor functions , 1993 .

[8]  J. Lemaître.  A CONTINUOUS DAMAGE MECHANICS MODEL FOR DUCTILE FRACTURE , 1985 .

[9]  R. Borst,et al.  Studies in anisotropic plasticity with reference to the Hill criterion , 1990 .

[10]  Adiabatic shear band localization in elastic-plastic damaged solids , 1992 .

[11]  C. Miehe,et al.  On the representation of Prandtl-Reuss tensors within the framework of multiplicative elastoplasticity , 1994 .

[12]  Robert L. Taylor,et al.  Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems☆ , 1993 .

[13]  R. Hill.  A general theory of uniqueness and stability in elastic-plastic solids , 1958 .

[14]  R. Hill.  Acceleration waves in solids , 1962 .

[15]  E. Stein,et al.  On a unified approach to the description of phase transitions and strain localization , 1996, Archive of Applied Mechanics.

[16]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[17]  Christian Miehe,et al.  Associative multiplicative elasto-plasticity: Formulation and aspects of the numerical implementation including stability analysis , 1994 .

[18]  P. Steinmann.  An improved FE expansion for micropolar localization analysis , 1994 .

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

[20]  J. Prévost,et al.  Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples , 1990 .

[21]  Ioannis Vardoulakis,et al.  Gradient dependent dilatancy and its implications in shear banding and liquefaction , 1989 .

[22]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[23]  J. Rice.  Localization of plastic deformation , 1976 .

[24]  R. Borst.  SIMULATION OF STRAIN LOCALIZATION: A REAPPRAISAL OF THE COSSERAT CONTINUUM , 1991 .

[25]  E. Stein,et al.  A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains , 1996 .

[26]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[27]  J. C. Simo,et al.  Associated coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation , 1992 .

[28]  J. Hadamard,et al.  Leçons sur la propagation des ondes et les equations de l'hydrodynamique , 2015 .

[29]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[30]  Paul Steinmann,et al.  Micropolar elastoplasticity and its role in localization , 1993 .

[31]  E. Aifantis.  On the Microstructural Origin of Certain Inelastic Models , 1984 .

[32]  Zenon Mróz,et al.  Finite element analysis of deformation of strain‐softening materials , 1981 .

[33]  J. C. Simo,et al.  Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes , 1992 .

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

[35]  Elias C. Aifantis,et al.  The physics of plastic deformation , 1987 .

[36]  Paul Steinmann,et al.  On the numerical treatment and analysis of finite deformation ductile single crystal plasticity , 1996 .

[37]  René de Borst,et al.  A generalisation of J 2 -flow theory for polar continua , 1993 .

[38]  J. C. Simo,et al.  An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids , 1993 .

[39]  Zdeněk P. Bažant,et al.  Non-local yield limit degradation , 1988 .

[40]  Jean Lemaitre,et al.  Coupled elasto-plasticity and damage constitutive equations , 1985 .

[41]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[42]  Ted Belytschko,et al.  Wave propagation in a strain-softening bar: Exact solution , 1985 .

[43]  K. Willam,et al.  Localization within the Framework of Micropolar Elasto-Plasticity , 1991 .

[44]  Kenneth Runesson,et al.  Discontinuous Displacement Approximation for Capturing Plastic Localization , 1993 .

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

[46]  Paul Steinmann,et al.  Performance of enhanced finite element formulations in localized failure computations , 1991 .

[47]  E. Stein,et al.  Comparison of different finite deformation inelastic damage models within multiplicative elastoplasticity for ductile materials , 1994 .

[48]  M. Ortiz,et al.  A finite element method for localized failure analysis , 1987 .

[49]  Christian Miehe,et al.  Post-critical discontinuous localization analysis of small-strain softening elastoplastic solids , 1994, Archive of Applied Mechanics.

[50]  Hans Muhlhaus,et al.  Application of Cosserat theory in numerical solutions of limit load problems , 1989 .

[51]  C. Miehe,et al.  Aspects of the formulation and finite element implementation of large strain isotropic elasticity , 1994 .

[52]  Paul Steinmann,et al.  Micropolar Elasto-Plasticity and Its Role in Localization Analysis , 1991 .

[53]  E. Stein,et al.  On the localization analysis of orthotropic hill type elastoplastic solids , 1994 .

[54]  Gilles Pijaudier-Cabot,et al.  Strain localization and bifurcation in a nonlocal continuum , 1993 .