Local Goal-Oriented Estimation of Modeling Error for Multi-Scale Modeling of Heterogeneous Elastic Materials

We consider the multi-scale analysis of the mechanics of multiphase composites with complex microstructure, based on the Goal-Oriented Adaptive Modeling method [1-10]. The underlying approach of this method is to perform an initial analysis using homogenized, or effective, properties and sequentially improve these by adding only enough of the actual microstructure to control the modeling error in a user-specified quantity of interest. The quantification of the modeling error is established by providing residual-based a posteriori error estimates [11]. However, this involves solving an additional global dual problem and computing global integrals of governing residual functionals. In the case of multiphase composite materials this estimation process can be computationally prohibitive. We therefore propose a technique for local, a posteriori estimation of the modeling error. It requires solving a local dual problem, of computationally small size, and computing local residual integrals. We introduce this new approach for the analysis of linear elastostatics problems of multiphase composites and show two-dimensional numerical verifications.