Kinematic Description of Damage

Abstract

In this paper the kinematics of damage for finite elastic deformations is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. However, the absence of the kinematic description of damage deformation leads one to adopt one of the following two different hypotheses. One uses either the hypothesis of strain equivalence or the hypothesis of energy equivalence in order to characterize the damage of the material. The proposed approach in this work provides a relation between the effective strain and the damage elastic strain that is also applicable to finite strains. This is accomplished in this work by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. The proposed approach shows that it is equivalent to the hypothesis of energy equivalence for finite strains. In this work, the damage is described kinematically in the elastic 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. The constitutive equations of the elastic-damage behavior are derived through the kinematics of damage using the simple mapping instead of the other two hypotheses.