Multiscale analysis of heterogeneous brittle materials using domain decomposition techniques

Abstract

In this contribution we present a multiscale framework for the analysis of brittle materials based on domain decomposition approaches. In particular, the FETI (Finite Element Tearing and Interconnecting) [1] method is selected to solve the decomposed structure. We start our analysis at a coarse level were effective properties are assigned to the homogeneous bulk. Using indicators, based on the constitutive model, we predict the moment at which non-linearities start int a certain domain (i.e. growth and propagation of damage). A zoom-in technique based on mesh refinement is applied to these domains and the underlying mesostructure is accounted for during the non-linear regime. The methodology proves to be a valuable application of the existing divide and conquer approaches for those materials that show localized failure phenomena. In these situations, computations need to be carried at a higher resolution level at places where the main non-linearities appear in order to accurately capture the global response.