ABSTRACT
In this chapter, the kinematics of damage for finite strain elasto-plastic deformation is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. In the absence of the kinematic description of damage, deformation leads one to adopt one of the following two different hypotheses for the small deformation problems. One uses either the hypothesis of strain equivalence or the hypothesis of energy equivalence in order to characterize the damage in the material. The proposed approach in this chapter provides a general description of kinematics of damage applicable to finite strains. This is accomplished by directly considering the kinematics of the deformation field and, furthermore, noting that it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. In this chapter, damage is described kinematically in both the elastic domain and the plastic domain using the fourth-order damage effect tensor, which is a function of the second-order damage tensor. The damage effect tensor is explicitly characterized in terms of a kinematic measure of damage through a second-order damage tensor. Two kinds of second-order damage tensor representations are used with respect to two reference configurations. The finite elasto-plastic deformation behavior with damage is also viewed here within the framework of thermodynamics with internal state variables. Using the consistent thermodynamic formulation, one introduces separately the strain due to damage and the associated dissipation energy due to this strain.
