Analytical and numerical comparison of discrete damage models with induced anisotropy

•New method to analyze and select anisotropic damage model.•Comparison of damage effect of selected models for a Vosges sandstone.•VDT model capacity in managing independently the damage effect on elastic properties.•Conditions are proposed to ensure the increase of contraction coefficient.

Quasi-brittle materials are modeled taking into account the anisotropic damage and its unilateral character. Among the models, proposed in the literature, a first selection has been made. The attention is thus restricted to models where the damage is managed by a discrete sum of its effects along fixed directions. The influence of the basic assumptions of the selected models are compared. Thus, models are at first expressed both into the Kunin and Walpole tensor decompositions to highlight the damage effects on each stiffness tensor component. A numerical study illustrates the effect of a damage effect on engineering parameters sensitivity and compares the versatility of those models. This work shows that the microplane framework is the most versatile, against Poisson’s ratio damage, while using the Volumetric Deviatoric Tangential (VDT) decomposition.