A Consistent Anisotropic Brittle Damage Model Based on Growing Elliptical Microcracks

It is known from experiments that all materials, and in more special case brittle materials, under general loading conditions develop anisotropic damage [1]. For a given stress state, materials damaged by microcracks in general accumulate additional damage through the growth of these microcracks. Considering this the concern of this paper is to provide a consistent, continuum damage model based on the micromechanical framework and the local anisotropy (orthotropy) induced by kinking and growing elliptical and/or circular microcracks. For clarity purposes and to explain the main issues of the proposed model in a more clear mathematical way, the complexity of the proposed damage model is reduced here by leaving out the thermal effects and other non-mechanical phenomena. Strains and rotations are assumed to be small; hence the framework of linear elastic fracture mechanics can be applied. Furthermore, viscous effects and permanent deformations are neglected and the material behavior is assumed to be linear elastic in its pristine state. The small strain assumption, and the lack of permanent deformations in this model makes it suitable to show the evolution of damage in structures with brittle and quasi-brittle fracture behavior experiencing high-cycle fatigue.