Stochastic multiscale modeling with random fields of material properties defined on nonconvex domains

A methodology to model and generate spatially dependent material uncertainties in stochastic multiscale analysis is proposed. The approach consists in defining non-Gaussian random fields through transport maps acting on Gaussian fields, defined by appropriately filtering a Gaussian white noise. In contrast to standard covariance-based representations, the proposed strategy can efficiently accommodate the case of fields with anisotropic correlation structures on nonconvex domains. This case is especially relevant to computational homogenization involving random microstructures with connected phases. The theoretical stochastic framework is first laid down. A numerical application associated with a polydisperse random microstructure is then presented to illustrate various aspects of the method.