Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization

Abstract

We present a multiscale finite element approach for composite structure analysis, applying reduced order homogenization to obtain an accurate surrogate model for microscale RVE computations and establishing macroscale mesh adaptivity towards an error control of a user-defined quantity of interest. By means of the so-called nonuniform transformation field analysis, reduced variables are deduced from a space–time decomposition of inelastic strain fields. Considering the macroscopic dissipation power as a volume-averaged microscopic dissipation power, closed-form macroscale constitutive relations are established, thus resulting into a reduced order homogenization problem. For ease of error estimate, we propose a multifield formulation for the reduced order problem. Based on duality techniques, a backward-in-time dual problem is derived from a Lagrange method, leading to error representations aiming at the quantity of interest. Accordingly, an efficient error estimator combined with a patch recovery technique avoiding nonlinear computations is proposed. The effectiveness of the resulting adaptive algorithm is illustrated by several numerical examples w.r.t. a prototype model.