Mesh sensitivity in peridynamic simulations

In this work, we investigate the suitability of several meshing strategies for use with a common peridynamics solution scheme. First, we use a manufactured solution to quantify the influence of different meshes on the accuracy and conditioning of a nonlocal boundary value problem in one and two dimensions. We explore convergence behavior, the effects of model parameters, and sensitivity to perturbations. We then apply the same meshing strategies to a three-dimensional impact simulation that employs the full peridynamic mechanical theory. We present a qualitative comparison of the fracture patterns that result, and suggest best practices for generating meshes that lead to efficient, high-quality numerical simulations of peridynamic models.