Asymptotically Compatible Schemes for Peridynamics Based on Numerical Quadratures

Abstract

We present some studies of numerical schemes for nonlocal peridynamic and nonlocal diffusion models. We describe asymptotically compatible (AC) schemes recently developed for robust discretizations of nonlocal models. The AC schemes for peridynamic models provide convergent approximations to nonlocal models associated with fixed horizon parameter as well as their limiting local models. We illustrate what quadrature based discretizations can be AC schemes and what may fail to be AC.