On-the-fly multiscale analysis of composite materials with a Generalized Finite Element Method

Abstract

A multiscale computational framework to capture stress concentrations and localized nonlinearity in composite structures is presented. An enriched approximation space, constructed using the generalized finite element method (GFEM), is used to incorporate nonlinear, heterogeneous material behavior into coarse-scale models on the fly. Enrichment functions are constructed using the GFEM with global–local enrichment functions (GFEM${}^{gl}$). The auxiliary local problems associated with the GFEM${}^{gl}$ also define fine-scale constitutive behavior that is inherited by the coarse global problem. This allows a coarse homogenized global problem to learn about material heterogeneity and/or nonlinearity on the fly, considerably increasing the flexibility of the method. On top of the explicit definition of heterogeneity in local problems, the locally defined constitutive law can incorporate further levels of heterogeneity that are not explicitly modeled at the global scale. The proposed GFEM${}^{gl}$ comes with the efficiency and scalability characteristic of the method and greatly increases the flexibility when applied to heterogeneous structures with localized material nonlinearity.