Computation and simulation of reliability parameters and their variations in heterogeneous materials Original Research Article

Two numerical methods for reliability assessment for composite microstructures under arbitrary loading are presented: a Monte Carlo (MC) technique that assigns discrete failure probabilities from local stresses and empirical failure probabilities, and a parametric probability product (PP) method where the joint probability of survival is from a product over a set of heterogeneous finite elements. The two methods are verified for known cases and then applied to random composite microstructures that are not amenable to direct analysis. While the MC method is computationally more expensive and less accurate than the PP method, it produces a distribution of failure predictions. The distribution places confidence intervals on survival probabilities or estimates for the number of physical experiments required to predict Weibull parameters. A composite microstructure does not have a failure distribution of the same form as its homogeneous composite parts, but its form is readily understood.