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

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.