A probabilistic peridynamic framework with an application to the study of the statistical size effect

Abstract

The high computational expense of peridynamic models remains a major limitation, hindering ‘outer-loop’ applications that require a large number of simulations, for example, uncertainty quantification. This contribution presents a framework that makes such computations feasible. By employing a Multilevel Monte Carlo framework, where the majority of simulations are performed using a coarse mesh, and performing relatively few simulations using a fine mesh, a significant reduction in computational cost can be realised, and statistics of structural failure can be estimated. The maximum observed speed-up factor is 16 when compared to a standard Monte Carlo estimator, thus enabling the efficient forward propagation of uncertain parameters in a computationally expensive peridynamic model. Furthermore, the multilevel method provides an estimate of both the discretisation error and sampling error, thereby improving confidence in numerical predictions. The performance of the approach is demonstrated through an examination of the statistical size effect in quasi-brittle materials.