An Adaptive Multiscale Finite Element Method for Large Scale Simulations

Abstract : This report presents recent advances of a Generalized Finite Element Method (GFEM) for multiscale non-linear simulations. This method is able to handle complex non-linear problems such as those exhibiting softening in the load-displacement curve. Cohesive fracture models lead to this class of non-linear behavior, which are significantly more computationally expensive than in the case of linear elastic fracture mechanics. In this novel GFEM, scale-bridging enrichment functions are updated on the fly during the non-linear iterative solution process. Non-linear fine scale solutions are embedded in the global scale using the partition of unity framework of the GFEM. Damage information computed at fine-scale problems are also used at the coarse scale in order to avoid costly non-linear iterations at the global scale. This method enables high-fidelity nonlinear simulation of representative aircraft panels using finite element meshes that are orders of magnitude coarser than those required by available finite element methods. Another achievement of this project is the development of stable generalized finite element solution spaces for three-dimensional fracture problems. These spaces lead to systems of equations that are orders of magnitude better conditioned than in available GFEMs.