Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure

Abstract In this work, we present a finite element model capable of describing both the plastic deformation which accumulates during the hardening phase as the precursor to failure and the failure process leading to softening phenomena induced by shear slip lines. This is achieved by activating subsequently hardening and softening mechanisms with the localization condition which separates them. The chosen model problem of von Mises plasticity is addressed in detail, along with particular combination of mixed and enhanced finite element approximations which are selected to control the locking phenomena and guarantee mesh-invariant computation of plastic dissipation. Several numerical simulations are presented in order to illustrate the ability of the presented model to predict the final orientation of the shear slip lines for the case of non-proportional loading.

[1]  Milan Jirásek,et al.  Embedded crack model: I. Basic formulation , 2001 .

[2]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[3]  J. Oliyer.  Continuum modelling of strong discontinuities in solid mechanics using damage models , 1995 .

[4]  I. Stakgold.  Green's Functions and Boundary Value Problems , 1979 .

[5]  T. Belytschko,et al.  A finite element with embedded localization zones , 1988 .

[6]  Edward L. Wilson,et al.  A modified method of incompatible modes , 1991 .

[7]  M. A. Crisfield,et al.  Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics , 1997 .

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

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

[10]  Kenneth Runesson,et al.  Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain , 1991 .

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

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

[13]  J. Mandel.  Conditions de Stabilité et Postulat de Drucker , 1966 .

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

[15]  K. Bathe.  Finite Element Procedures , 1995 .

[16]  Giulio Alfano,et al.  An interface element formulation for the simulation of delamination with buckling , 2001 .

[17]  J. C. Rice,et al.  On numerically accurate finite element solutions in the fully plastic range , 1990 .

[18]  W. Spaans.  The finite element methods , 1975 .

[19]  Bernard D. Coleman,et al.  On shear bands in ductile materials , 1985 .

[20]  W. Gibbs,et al.  Finite element methods , 2017, Graduate Studies in Mathematics.

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

[22]  Adnan Ibrahimbegovic,et al.  Classical plasticity and viscoplasticity models reformulated: theoretical basis and numerical implementation , 1998 .

[23]  Milan Jirásek,et al.  Comparative study on finite elements with embedded discontinuities , 2000 .

[24]  C. Truesdell,et al.  The Non-Linear Field Theories of Mechanics , 1965 .

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

[26]  Ted Belytschko,et al.  Continuum Theory for Strain‐Softening , 1984 .

[27]  R. Borst,et al.  Localisation in a Cosserat continuum under static and dynamic loading conditions , 1991 .

[28]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .