Cracking of plates with randomly distributed holes by a maximum entropy method

It has recently been shown that fracture response of nominally identical elastic-brittle (epoxy) as well as ductile (aluminum) sheets, each containing randomly distributed circular holes, is non-unique. This non-uniqueness pertains, in particular, to the resulting fracture patterns and effective stress-strain curves, whereby both of these characteristics display considerable scatter. This result points to the significant influence which microscale random noise in material parameters may have on the global, macroscopic behavior. In this paper we formulate, on the basis of a maximum entropy method, a stochastic fracture mechanics model for this class of problems. The method is based on the statistics of experimental data, obtained for a number of specimens, involving the inter-hole crack lengths and their angles. It allows prediction of probability distributions of damage responses and patterns of Gibbs ensembles of random hole systems such as, for example, porous materials with millions of voids.