Discrete approach for modelling quasi-brittle damage: conditions on the set of directions

Abstract The aim of this Note is to investigate the discrete approach of anisotropic damage by microcracking by specifying the choice of the set of fixed directions that are to be effectively employed. Three conditions are presented, concerning the description of any damage configuration, and in particular isotropic and transversely isotropic ones. These conditions are given at two different orders in orientation (order 2 and order 4), as both tensorial terms intervene in the thermodynamic potential. The results show that the second order conditions are sufficient to represent a configuration of open microcracks, whereas fourth order conditions are necessary to represent a configuration of closed ones. To cite this article: R. Bargellini et al., C. R. Mecanique 335 (2007).