A multimesh finite element method for integral nonlocal elasticity using mesh-decoupling technique

Abstract

This study presents a generalized multimesh nonlocal finite element method (M2-FEM) that addresses several long-standing challenges in the numerical simulation of Eringen’s integral elasticity theories, often used to model nonlocal effects. The major challenges in the numerical simulation of integral boundary value problems are primarily rooted in the coupling of the spatial discretization of the global (parent) and integral (child) domains, which severely restricts both the applicability and the computational efficiency of existing algorithms by imposing an implicit trade-off between the accuracy of the child domain and the resources required by the overall parent domain. One of the defining contributions of this study consists in the development of a mesh-decoupling technique that generates isolated sets of meshes such that the parent and child domains can be discretized and approximated independently. This mesh-decoupling has multi-fold advantages on the simulation of integral theories such that, when compared to existing state-of-the-art techniques, the proposed algorithm achieves a greater ability to adopt generalized integral kernel functions, the ability to handle non-regular (non-rectangular) domains via unstructured meshing, and simultaneously better numerical accuracy and efficiency (hence allowing greater flexibility in both mesh size and computational cost trade-off decisions). Both benchmark studies and several case studies are conducted to assess the effectiveness of M2-FEM. Simulation results confirm that M2-FEM can accurately simulate integral nonlocal problems and demonstrate its multi-fold computational advantages over existing mesh-coupling-based nonlocal finite element methods. Overall, the proposed M2-FEM algorithm is very general and it can be applied to a variety of integral theories, even beyond nonlocal elasticity.