A probabilistic nonlocal model for crack initiation and propagation in heterogeneous brittle materials

A probabilistic damage model is developed to study crack initiation and growth in quasi-brittle materials. Two different thresholds are considered to describe these mechanisms. A Weibull model is used to account for the randomness of crack initiation(s) and then a fracture mechanics based threshold is considered to model crack propagation. The model is integrated in a finite element code via a nonlocal damage approach. A regularization operator based on a stress regularization is introduced. Both damage thresholds are checked using the regularized stress field to avoid mesh dependence. The interaction between propagating cracks and potential initiation sites is accounted for. Copyright (c) 2012 John Wiley & Sons, Ltd.