RANDOM STRUCTURE MODELS FOR COMPOSITE MEDIA AND FRACTURE STATISTICS

As a consequence of microstructural heterogeneities, fluctuations in the mechanical properties of materials are observed in experiments. This requires a probabilistic approach to relate the microstructure to the overall properties, and to predict scale effects in the fluctuations of properties. In this paper, the problem of the strength of materials is addressed, and various models of random structures developed for fracture statistics are introduced. As any fracture criterion is sensitive to microstructural heterogeneities, such as flaws with low strength, or defects including a local stress concentration, large effects of small scale heterogeneities are observed for fracture phenomena. The approach combines the selection of appropriate fracture criteria and random structure models. It enables us to predict the probability of fracture of heterogeneous media under various loading conditions.