Coupling of an atomistic model and bond-based peridynamic model using an extended Arlequin framework

Abstract

A general nonlocal coupling technique between an atomistic (AM) model and the bond-based peridynamic (PD) model is proposed, based on the Arlequin framework. This technique applies the complementary weight function and constraint conditions to transmit energies through the overlapping region between the AM and PD regions. We extend the original Arlequin framework to discrete cases by redefining constraint conditions by the peridynamic differential operator, which enables the interpolation and corresponding derivative of scattered data. Besides, the preconditioning of calibration for the PD effective micromodulus is implemented to guarantee the equilibrium of energy. One-dimensional benchmark tests investigate the coupling effects influenced by several key factors, including the coupling length, weight function, grid size and horizon in the PD model, and constraint conditions. Two- and three-dimensional numerical examples are provided to verify the applicability and effectiveness of this coupling model. Results illustrate this AM–PD coupling model takes the mutual advantages of the computational efficiency of PD model and the accuracy of AM model, which provides a flexible extension of the Arlequin framework to couple particle methods.