On a kinetic formulation of elasto-viscoplasticity

Abstract

A kinetic formulation of elasto-viscoplasticity is proposed. It consists ofa non-linear Maxwell-like viscoelastic constitutive equation (CE) that describes the evolution of the recoverable (elastic) part of the total Finger strain tensor, a thermodynamic formulation of stress tensor dependence on the elastic strain tensor, and a kinetic equation for a scalar “bonding” factor. The set of CEs does not contain any mathematical yield criterion but predicts anisotropic yield values for stress as a transition from solid-like deformations to flow through a bifurcation. The set of CEs proposed is shown to be globally Hadamard stable. The dissipative stability is also discussed briefly. In the case when the elastic strains are sufficiently small, the second-order approach is developed. Within this approach, several problems of simple shearing are analyzed to illustrate the model behavior.