Finite strain plasticity models revealed by symmetries and integrating factors: The case of Dafalias spin model

Abstract

We consider a rigid plastic constitutive model with linear kinematic hardening, relying on the concept of constitutive spin introduced by Dafalias (1985a,b) to describe the evolution of the orientation of the material texture. A more general writing of the constitutive spin using representation theorems for second order tensors is proposed, involving arbitrary functions of the tensor invariants. The computation of continuous symmetries and integrating factors of the resulting system of differential equations leads to a classification of cases, in terms of the constitutive functions, focusing on simple planar shear. Exact and numerical solutions for stress versus time are obtained for some objective rates. The comparison of the evolution of the integrated stress components allows drawing some conclusion as to the more suitable objective rates. Dynamical invariants computed in terms of the components of the back stress tensors and of the shear strain allow to directly evaluate the dynamical response of the material in terms of the phase portrait in the space of independent components of the back stress tensor. Fundamental principles of irreversible thermodynamics are used as a filtering mechanism for the constitutive models revealed by symmetries and invariants, leading to the choice of constitutive models that satisfy all proposed criteria. These models involve a non-linear dependence of the plastic spin on the back stress.