Statistics of strength of elastic-brittle composite materials

We study crack patterns and effective stress-strain response in unidirectional fiber-matrix composites subjected to out-of-plane and in-plane loading. The fibers are aligned in the longitudinal direction and arranged randomly, with no overlap, in the transverse plane. The fibers and the matrix are isotropic and elastic-brittle, which allows a parametrization of a wide range of composites in terms of a stiffness ratio and a strain-to-failure ratio. The analysis is carried out numerically using very fine two-dimensional spring networks permitting simulation of the crack initiation and propagation by sequentially removing bonds which exceed a local fracture criterion. Particular attention is given to the effects of scale and geometric randomness in these composites. We consider several `windows of observation' (scales) and study crack patterns, types of constitutive responses, and statistics of the corresponding scale dependent effective elastic stiffness and strength of such composites.