PERTURBATION-BASED SURROGATE MODELS FOR DYNAMIC FAILURE OF BRITTLE MATERIALS IN A MULTISCALE AND PROBABILISTIC CONTEXT

摘要

Localization of failure in many materials is associated with the heterogeneity in the material microstructure. Multiscale models often address this heterogeneity by passing field variables back and forth between a macroscale model and subscale analyses at each integration point. Although this technique is often effective, it can be extremely costly to perform distinct microscale analyses for every integration point in the domain. The proposed work uses a perturbation-based approach, conceptually similar to in situ adaptive tabulation, which provides a straightforward surrogate model that can be orders of magnitude more efficient than the microscale model. The approach is demonstrated specifically for models of dynamic brittle failure, in which crack populations are tracked from one load step to the next. Furthermore, following an approach similar to that used in perturbation -based stochastic finite elements, this technique streamlines the process of probabilistic characterization of the instantaneous stress and the uniaxial compressive strength. Numerical examples show that the approach is accurate and highly efficient when considering random perturbations in both the underlying flaw population and the strain history in these brittle materials.