A THERMODYNAMIC FORMULATION OF FINITE-DEFORMATION ELASTOPLASTICITY WITH HARDENING BASED ON THE CONCEPT OF MATERIAL ISOMORPHISM

This paper presents a thermodynamic formulation of a model for finite deformation of materials exhibiting elastoplastic material behaviour w ith non-linear isotropic and kinematic hardening. Central to this form ulation is the notion that the form of the elastic constitutive relati on be unaffected by the plastic deformation or transformation in the m aterial, as commonly assumed in particular in the context of crystal p lasticity. When generalized to the phenomenological context, this impl ies that the internal variable representing plastic deformation is an elastic material isomorphism. Among other things, this requirement on the plastic deformation leads directly to the standard elastoplastic m ultiplicative decomposition of the deformation gradient. In addition, a dependence of the plastic part of the free energy on the plastic def ormation itself yields a thermodynamic form for the centre of the elas tic range of the material, i.e. the back stress. Finally, we show how this approach can be applied to formulate thermodynamic forms for line ar, and non-linear Armstrong-Frederick, kinematic hardening models. (C ) 1998 Elsevier Science Ltd. All rights reserved.