Efective properties of elastic solids with randomly distributed microcracks

Homogenization methods are applied mainly to materials with a periodic microstructure. A random material can be defined as a material with microstructure described by random functions, or more generally, random fields. There are two main approaches to solving the problem of macroscopic description of media with random structure. One is based on the theory of partial differential equations with rapidly and randomly fluctuating coefficients. The second approach is based on the theory of random integral functionals. Both approaches exploit an analogy between periodicity and stochastic homogeneity and ergodicity. Homogenization of an elastic solid weakened by randomly distributed microcracks was performed.