Multiscale numerical modeling of deformation responses of heterogeneous materials

Abstract

A multiscale computational algorithm employing the second-order computational homogenization under assumption of large strain is presented. A macro-micro transition procedure has been derived, where the discretization at the macrolevel has been performed by the newly developed C 1 continuity displacement based finite elements. The representative volume element at the microlevel is discretized by using standard C 0 continuity finite elements. The performed verifications of the proposed C 1 finite element formulation show an advantage in comparison to available finite elements based on mixed formulations. In order to improve numerical efficiency of the computational procedures, the new algorithms are embedded into the finite element program Abaqus. The performance of the presented multiscale homogenization approach is demonstrated in numerical examples, where the elastoplastic deformation responses are displayed.