On the structure of anisotropic damage yield criteria

Abstract

This paper addresses explicit yield criteria coupled with anisotropic damage in Cauchy stress space for materials initially obeying J 2 plasticity. It is shown in this paper that the original Kachanov–Rabotnov damage model is inherently microplane-based and generally cannot ensure the existence of the effective stress tensors. It is further assumed that the effective stress approach still holds if the effective stress tensor is replaced by the effective stress vector. The effective counterpart of J 2 is calculated based on the generalized effective stress approach and the hypothesis of mean square shear stress averaged over all microplanes for J 2. It is revealed that the effective counterpart of J 2 takes the form of Hill [Hill, R., 1950. The Mathematical Theory of Plasticity, Clarendon Press, Oxford] anisotropic yield function in Cauchy stress space. The six parameters of Hill [Hill, R., 1950. The Mathematical Theory of Plasticity, Clarendon Press, Oxford] anisotropic yield function can be determined uniquely by a fourth-order fabric tensor.