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 with non-linear isotropic and kinematic hardening. Central to this formulation is the notion that the form of the elastic constitutive relation be unaffected by the plastic deformation or transformation in the material, as commonly assumed in particular in the context of crystal plasticity. When generalized to the phenomenological context, this implies 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 multiplicative decomposition of the deformation gradient. In addition, a dependence of the plastic part of the free energy on the plastic deformation itself yields a thermodynamic form for the centre of the elastic range of the material, i.e. the back stress. Finally, we show how this approach can be applied to formulate thermodynamic forms for linear, and non-linear Armstrong-Frederick, kinematic hardening models.