Accurate absorbing boundary conditions for two-dimensional peridynamics

The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) for the two-dimensional peridynamics equation of motion which describes nonlocal phenomena arising in continuum mechanics based on integrodifferential equations. To this end, a full discretization of the system is used based on a Crank-Nicolson scheme in time and an asymptotically compatible scheme in space. Recursive relations for the Green's functions are then derived and numerically used to evaluate the nonlocal ABCs. In particular, these absorbing boundary conditions solve the corner reflection problem with high precision. The stability of the complete fully discretized scheme is stated and numerical examples are finally reported to demonstrate the validity of the resulting ABCs.