Hierarchical modeling of heterogeneous structures driven by a modeling error estimator

Homogenized models are widely used in multiscale analysis for their computational efficiency, but they often fail to provide sufficient accuracy in regions exhibiting high variations in the solution fields. One way to address this limitation is to adaptively couple the homogeneous model with a full field, heterogeneous one in designated zones of interest. Within the framework of finite-element based higher-order asymptotic homogenization, this work introduces a modeling error estimator in order to detect regions where refining the material model is necessary. We also analyze the competition between discretization and modeling errors. We finally propose a multiscale enhancement of the classical displacement-based submodeling technique in order to adequately couple the homogeneous and heterogeneous domains. The promise of the proposed methods and the overall associated strategy is illustrated on various numerical examples of elastic fiber–matrix composites.