Multi-adaptive coupling of finite element meshes with peridynamic grids: robust implementation and potential applications

Abstract

Coupling of methods based on the classical continuum mechanics (CCM), with peridynamic (PD) models is a recent hot topic in the realm of computational mechanics. In the coupled models, to optimize the usage of computational resources, usually the application of PD (the more demanding procedure) is restricted to critical areas of the domain affected by discontinuities such as propagating cracks. The remaining parts of the domain are described by a more efficient CCM-based model such as the finite element method (FEM). Here, we develop a coupled FEM/PD model for dynamic fracture modeling. The proposed method simultaneously features the following: (1) it can adaptively change the coupling configuration throughout the simulation such that only critical zones, on the verge of crack nucleation/propagation, are tackled by the PD procedure, and (2) it appropriately supports different grid spacing of PD and FEM parts. We refer to a model possessing both the features as multi-adaptive. This is crucial for a highly efficient coupling scheme. The performance of the proposed method is analyzed in terms of accuracy and computational efficiency through different numerical examples. The results show that the proposed method is superior to using a refined PD model, since it provides the same level of accuracy at a much lower computational cost. As a novel application, we present the promising results of a crack propagation problem in an unbounded domain, solved using classical artificial boundary conditions on an outer FEM layer.