Nonlocal model for size effect in quasibrittle failure based on extreme value statistics

A nonlocal generalization of Weibull theory is presented to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture. The probability of failure at a material point is assumed to be a power function of the average strain in the neighborhood of that point. For normal sizes, the deterministic theory is found to dominate the mean response and govern the size effect. But the probabilistic theory can provide the entire probability distribution. For extremely large beam sizes, the statistical size effect dominates and the mean prediction approaches asymptotically the classical Weibull size effect. This fundamental feature is discussed in relation to the existing stochastic finite element models. Comparison to the existing test data demonstrates a good agreement with the theory.