The kinematics of damage for finite-strain elasto-plastic solids

In this paper the kinematics of damage for finite strain, elasto-plastic de formation is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum dama ge mechanics. In the absence of the kinematic description of damage deforma tion leads one to adopt one of the following two different hypotheses for t he small deformation problems. One uses either the hypothesis of strain equ ivalence or the hyphothesis of energy equivalence in order to characterize the damage of the material. The proposed approach in this work provides a g eneral description of kinematics of damage applicable to finite strains. Th is is accomplished by directly considering the kinematics of the deformatio n field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. In t his work, the damage is described kinematically in both the elastic domain and plastic domain using the fourth order damage effect tensor which is a f unction of the second-order damage tensor. The damage effect tensor is expl icitly characterized in terms of a kinematic measure of damage through a se cond-order damage tensor. Two kinds of second-order damage tensor represent ations are used in this work with respect to two reference configurations. The finite elasto-plastic deformation behavior with damage is also viewed h ere within the framework of thermodynamics with internal state variables. U sing the consistent thermodynamic formulation one introduces seperately the strain due to damage and the associated dissipation energy due to this str ain. (C) 1999 Elsevier Science Ltd. All rights reserved.