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.
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The formal structure of a large class of standard damage models is being revisited. Particular attention is paid to the dependence of damage convex on the damage (internal) variables themselves. This dependence complicates the discussion about the existence and uniqueness conditions since the rate of internal variable is no longer a solution of a symmetric variational inequality. The alternative formulation is put forward involving a complementary set of internal variables. This method, leading to a fixed damage convex, brings back the rate response to an incremental behavior relevant to the generalized standard formalism. Some non-fixed convex models are replaced in the framework of damage models with fixed convex.
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