Modelling of anisotropic damage by microcracks: towards a discrete approach

Modelling of anisotropic damage by microcracks remains a pivotal topic of Damage Mechanics. Many models are built employing a single second-order tensor damage variable D and its spectral decomposition. However, some inconveniences are encountered such as non-uniqueness of the free energy or decomposition of the strain tensor. This paper first reconsiders the anisotropic damage definition; a discrete approach, which introduces nine microcrack densities associated with nine fixed directions, is presented. This definition permits to represent essential phenomena concerning quasi-brittle materials behaviour: the induced anisotropic degradation of elastic properties and the unilateral effect are notably described. In addition, the quoted inconveniences are avoided.