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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.