Computations of effective moduli for microcracked materials: A boundary element approach

The paper deals with a computational investigation on effective moduli of brittle materials weakened by microcracks. The study is based on a suitable adaptation of an indirect boundary element method, namely the displacement discontinuity method. Various aspects of microcracks size and orientation are investigated. For tensile loading (open cracks), the numerical results show good agreement with the classical non-interacting cracks approximation. Comparisons with some not fully random configurations are also presented. When crack-boundary interactions are taken into account, the results agree rather well with the differential approximation, but calculations under compressive loadings are much more complicated because of friction and sliding on crack faces, so an iterative algorithm for sliding and frictional cracks is used. The effective compliance in this case shows very little increase compared with the case of tensile loadings. Comparisons with some theoretical approximations are presented.