A microplane-based anisotropic damage effective stress

The Kachanov-Rabotnov damage effective stress is a fundamental concept in continuum damage mechanics. Controversies remain over the multiaxial generalization of the Kachanov-Rabotnov effective stress, especially when anisotropic damage effects occur. From a microplane point of view, we show that an anisotropic Kachanov-Rabotnov effective stress cannot simply be defined as a Cauchy-like stress tensor, namely a symmetric tensor of order two, but is essentially a vector-valued orientation distribution function. The practical effective stress tensor is identified by the second-order fabric tensor of the vector-valued Kachanov-Rabotnov stress orientation distribution function. The proposed model encompasses a wide range of classical models and thus clarifies the presuppositions of the models at a microplane level. We also prove the positive definiteness of the fourth-order damage effect tensor and provide a sufficient condition for its Voigt symmetry.