HYPERELASTIC MODELS FOR ELASTOPLASTICITY WITH NONLINEAR ISOTROPIC ANDKINEMATIC HARDENING AT LARGE-DEFORMATION

This work is concerned with the formulation of hyperelaslic-thermodyna mic-based. models for associated elastoplasticity with non-linear isot ropic and kinematic hardening valid for both large elastic and large p lastic deformation. On this basis, one can then introduce explicitly t he assumptions of (1), small incremental plastic deformation, and (2), small elastic strain, into the general model and obtain special cases whose behaviour corresponds to that of various classical hypoelastic formulations. In particular, these are obtained on the basis of two di fferent thermodynamic formulations for kinematic hardening with respec t to the intermediate configuration. The simplest of these, in which t he plastic part of the free energy does not depend explicitly on the p lastic deformation, leads for example to Jaumann- or Green-Naghdi-hypo elastic-type behaviour for linear kinematic hardening in simple shear. In particular, the former case is obtained in this context when the p lastic spin is assumed constant and equal to zero, and the latter case when the plastic rotation is assumed constant and equal to the identi ty. Allowing the plastic part of the free energy to depend explicitly on the plastic deformation yields the second thermodynamic model for k inematic hardening considered in this work. Here, again in the special case of linear hardening, Oldroyd-like behaviour for the shear stress and back stress, but not for the normal stress, is obtained in simple shear. (C) 1998 Elsevier Science Ltd. All rights reserved.