Numerical tools for improved convergence of meshfree peridynamic discretizations

Abstract

Peridynamic models have been employed to simulate a broad range of engineering applications concerning material failure and damage, with the majority of these simulations using a meshfree discretization. This chapter reviews that meshfree discretization, related issues present in peridynamic convergence studies, and possible remedies proposed in the literature. In particular, we discuss two numerical tools, partial-volume algorithms and influence functions, to improve the convergence behavior of numerical solutions in peridynamics. Numerical studies in this chapter involve static and dynamic simulations for linear elastic state-based peridynamic problems.