Modelling of anisotropic damage by microcracks: towards a discrete approach. (English) Zbl 1106.74007

Summary: Modeling 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 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 material behaviour: the induced anisotropic degradation of elastic properties and the unilateral effect are notably described. In addition, the quoted inconveniences are avoided.


74A45 Theories of fracture and damage
74E10 Anisotropy in solid mechanics