Developing a stochastic model to predict the strength and crack path of random composites

We characterize fracture and effective stress-strain graphs in 2-D random composites subjected to a uni-axial in-plane uniform strain. The fibers are arranged randomly in the matrix. Both fibers and matrix are isotropic and elastic-brittle. We conduct this analysis numerically using a very fine two-dimensional triangular spring network and simulate the crack initiation and propagation by sequentially removing bonds which exceed a local fracture criterion. In particular, we focus on effects of scale (size of fibers) and geometric randomness in such composites. We consider several "windows of observation" (scales) and study crack patterns and types of constitutive responses. Based on that two stochastic micro-mechanic models are presented that can predict with confidence the failure probability of random matrix-inclusion composites.