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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.

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