Micromechanical anisotropic damage approach for understanding localized behavior of brittle materials under tension

While a number of micromechanical damage models have been proposed to delineate the damage and failure of brittle rocks from a multi-scale viewpoint, the localization behavior in the post-peak failure phase is far from being fully understood and well described. This study provides a plausible explanation and model description of this localization behavior by incorporating a localized damage criterion into the well-developed micromechanics-based elastic anisotropic damage model (ME-ADM). Different from ME-ADM, the proposed model (named LE-ADM) can describe a smooth transition from diffused damage to localized damage under tension-dominated stresses. After proposing a novel anisotropic damage decoupling algorithms, the numerical results of both the ME-ADM and LE-ADM are compared to the derived analytical solution and verified with experimental results. We find that the LE-ADM effectively captures more abrupt brittle fracture behavior under tension and the proposed numerical algorithm are efficient to guarantee a numerical convergence. Finally, the localization orientation predicted by the proposed model is verified by the classic Mohr’s maximization postulate method.