Use of isotropic thermoelasticity laws in finite deformation viscoplasticity models

We consider general finite deformation thermoviscoplasticity models and focus attention to the thermoelasticity laws involved in the constitutive theory. The goal is to show how such constitutive relations having forms as simple as possible may be defined with respect to both the plastic intermediate configuration and the actual configuration. In particular, using two families of strain and associated stress tensors, we arrive at two different thermoelasticity laws formulated with respect to the actual configuration. These are extensions to nonisothermal deformations of corresponding hyperelasticity laws introduced previously by Simo [1].