Concurrently Coupled Peridynamics/Finite Element Simulation Based on Nonlocal Matching Boundary Conditions

Abstract

A concurrent multiscale approach that integrates non-ordinary peridynamics (NOPD) with finite element method (FEM) has been established. The proposed approach features two main technical ingredients: Firstly, a Non-Local Matching Boundary Condition (NMBC) is developed for treating the numerical interface of NOPD/FEM. The NMBC is cast in the form of a parameterized expression that involves the displacements and their higher-order time derivatives of peridynamic (PD) nodes at the numerical interface. The corresponding parameters are solved by enforcing the dispersion relation from three versions of PD initially, i.e., bond-based (BBPD), ordinary peridynamics (OPD) and non-ordinary peridynamics (NOPD). The latter part of the research focuses primarily on NOPD for higher dimension simulations. The effectiveness of the NMBC is given for BBPD, OPD and NOPD for 1D simulations, NOPD for 2D simulations with unidirectional and multidirectional waves. A bridging scale decomposition employing a projection approach is then introduced in the concurrent multiscale discretization scheme to further facilitate the information passage between the PD and FEM simulations. To demonstrate the effectiveness of the coupling method, multiple benchmark examples in both 1D and 2D are presented.