A stable formulation of correspondence‐based peridynamics with a computational structure of a method using nodal integration

Abstract

In this paper, we lay out a variational framework for correspondence‐based peridynamic (PD) formulations of solid mechanics. Using the framework, we address the numerical instabilities of the original version of correspondence‐based PD by developing a natural stabilization technique that avoids costly bond‐associated approaches and retains the structure of a method with nodal integration. Accuracy, robustness, and efficiency of the proposed naturally stabilized correspondence‐based PD are demonstrated on several computational test cases ranging from linear elastostatics to large deformation elasto‐plasticity. The computational methodology developed is particularly effective for handling materials undergoing nearly‐incompressible deformations.