B. Svendsen, A THERMODYNAMIC FORMULATION OF FINITE-DEFORMATION ELASTOPLASTICITY WITH HARDENING BASED ON THE CONCEPT OF MATERIAL ISOMORPHISM, International journal of plasticity, 14(6), 1998, pp. 473-488
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.