Robust discretization of nonlocal models related to peridynamics

Abstract

We study some nonlocal models related to peridynamics. These models are parameterized by a horizon that serves as a length scale measuring the range of nonlocal interactions. We focus on robust numerical schemes that can approximate both nonlocal models and their local limits as the horizon parameter vanishes. A representative linear model is used as an illustration.We show the lack of robustness of some standard numerical methods and describe a remedy to get asymptotically compatible schemes by utilizing elements of the recently developed nonlocal vector calculus and nonlocal calculus of variations. Such findings may be useful to ongoing research on modeling and simulations of nonlocal and multiscale problems.