Large strain, two-scale computational approach using C1 continuity finite element employing a second gradient theory

A two-scale computational algorithm employing second-order computational homogenization under assumption of large strain is presented. A micro-macro transition has been proposed, where the C1 continuity displacement based finite element is used for discretization at the macrolevel, while the representative volume element at the microlevel is discretized by C0 continuity finite elements. The performed finite element verifications show an advantage in comparison to available finite element formulations. In order to improve numerical efficiency of the proposed computational procedures, the 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 considered and compared with the small strain analysis.