A multiscale method coupling peridynamic and boundary element models for dynamic problems

Abstract

A novel multiscale method coupling peridynamics (PD) and boundary element method (BEM) is proposed for dynamic problems. In the coupling model, the discontinuous behaviors of materials such as crack development and branching processes are simulated by PD while the boundary and infinite domain are modeled by time-domain BEM, which can take full advantage of their salient features. A general stiffness matrix is introduced in the coupling model to combine the PD and BEM governing equations in such a way that the continuity of displacement and the equilibrium of tractions at the PD-BEM interface are satisfied. A variable horizon method is developed to further eliminate boundary effects and ghost forces at the coupling interface between PD and BEM. Then, a concurrent coupling procedure of PD and BEM is established and its implementation is also introduced based on the dynamic explicit algorithm, i.e. the central difference method. The proposed coupling method is verified by comparing its predictions with those from analytical and experimental results. Numerical examples demonstrate the applicability of the proposed model for wave propagation, infinite domain and fracture problems under dynamic loads.