An Improved Two-Dimensional Micromechanical Theory for Brittle Solids with Randomly Located Interacting Microcracks

This paper presents applications of accurate orthogonal function approximation methods to the two-dimensional problems of brittle solids containing many randomly located (and possibly randomly oriented) and strongly interacting microcracks within the framework of micromechanics and ensemble-volume average approach. The randomly located and oriented two-crack interaction problems are solved by using the highly accurate Legendre and Tchebycheff orthogonal polynomials to any desired order. The complex stress potential method is subsequently employed to micromechanically derive microcrack opening displacements under complicated loadings due to microcrack interaction effects-including concentrated loadings, arbitrary loadings and polynomial loadings. Improved local ensemble-averaged and overall effective elastic compliances of brittle solids due to microcracks and their interactions are systematically constructed by using the pairwise microcrack interaction mechanism and the ensemble-volume average approach. A number of interesting analytical-numerical examples containing different random microcrack configurations are also presented to illustrate the capabilities of the proposed framework.