A framework for large strain elastic–plastic damage mechanics based on metric transformations

Abstract

A continuum elastic–plastic damage model employing irreversible thermodynamics and internal state variables is presented. The approach is based on a kinematic description using multiplicative decomposition of the metric transformation tensor into elastic and damage-plastic parts. Furthermore, undamaged configurations are introduced which are related to the damaged ones via associated metric transformations which allow for the interpretation as damage tensors. Thus, the damage tensor is explicitly characterized in terms of a kinematic measure of damage. This leads to the definition of appropriate logarithmic strain measures. Strain rates are shown to be additively decomposed into elastic, plastic and damage strain rate tensors. Moreover, based on the standard dissipative material approach and a generalized effective stress concept, work-conjugate stress tensors are introduced. Elastic and plastic constitutive equations are formulated in an effective stress space. A generalized macroscopic yield condition is employed and the evolution of the effective plastic part of the strain rate tensor is determined via a non-associated flow rule. Considering the damaged configurations a generalized damage criterion is formulated using stress components referred to the elastically unloaded (stress free) damaged configuration. The evolution of the damage part of the strain rate tensor is discussed in some detail. It is based on a damage potential function and takes into account isotropic as well as anisotropic effects.