On Damage Strain Energy Release Rate Y

In the application of the theory of damage mechanics to solve a wide range of practical engineering problems, a generalized formulation of damage strain energy release rate Y is required. This is because the damage strain energy release rate Y, which is the thermodynamic conjugate force of damage variable D, is used to derive damage evolution equation. For the case of isotropic damage, the damage variable is degenerated to a scalar. Accordingly, the derivation of the damage strain energy release rate is relatively straightforward. However, it is much more involved in the case of anisotropic damage. Currently, no such generalized form of the damage strain energy release rate is available. This paper is intended to present the development of three formulations of damage strain energy release rate based on three different forms of the damage effect tensor M(D) for which D is a second order symmetric tensor. The realization of the anisotropic damage strain energy rate formulations makes it possible to obtain the solution of practical structural problems where the service loading is often nonproportional.