An approximate scheme for considering effects of microcrack interaction on the overall constitutive relation of brittle solids under complex loading

Presented in this paper is a three-dimensional, micromechanical evolutionary damage model enabling the calculation of an overall constitutive relation of microcrack-weakened brittle materials under complex loading. An approximate scheme is proposed to determine the effects of microcrack interaction on the overall constitutive relation under complex loading. All microcracks are assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the same radius depending upon the actual damage state. This elastic moduli of this approximate effective medium can be calculated by the well-established Taylor's model, self-consistent method, differential method, or other effective medium methods. The effective compliance tensor uncluding the influences of microcrack interaction is formulated for brittle solids under arbitrary tensile loading. This approximate method improves the accuracy of the Taylor model by implementing the effects of microcrack interaction in the overall constitutive relation and avoids the cumbersome computation of the self-consistent method in general loading cases.