Micro-crack informed multi-scale damage model: Theory and computation

Abstract

A class of multi-scale damage models for the softening of the brittle solids induced by micro-cracks is proposed, in which the damage evolution is the direct consequence of the micro-crack propagation. The homogenization of stress and strain fields in the cracked unit cell yields the degradation tensor, and the equivalence between the averaged strain energy of the unit cell and the strain energy density of the homogenized material is demonstrated. This energy equivalence relationship is consistent with that obtained from asymptotic-based homogenization, and it serves as an energy bridging vehicle between damaged continua and cracked microstructure. Damage evolution equations are obtained by this energy-bridging method. The size effect of the homogenized damage law is also characterized through the unit cell analysis, and the results are used to eliminate the mesh dependencies in damage-induced strain localization problems.