Eshelby's stress tensors in finite elastoplasticity

Abstract

This work examines critically the role that the Eshelby (energy-momentum) tensor or its degenerate form, the Mandel stress, should logically play as the driving force in an invariant formulation of the thermomechanics of finite-strain elasto-plasticity. Here the stress measure of which Mandel advocated the use in elastoplasticity, is shown to coincide, up to a sign, with the quasi-static Eshelby stress tensor expressed in the elastically released intermediate configuration. The various “constitutive” representations for the plastic rate are then discussed in terms of various thermodynamically conjugate pairs of “forces” and “velocities” for anisotropic materials.