Stress-point method for stabilizing zero-energy modes in non-ordinary state-based peridynamics

Abstract

Non-ordinary state–based peridynamics is a promising continuum mechanics theory that combines non-local dynamics with conventional material models. Within this theory, the correspondence principle can be invoked to compute deformation gradients from the computed displacement fields. However, correspondence based models are prone to a zero-energy mode. This paper proposes the use of stress points to resolve this issue in the peridynamic family with nearest-neighbor discretizations. Each particle horizon is assigned with stress points at which derivatives of field variables are computed. The method is first demonstrated in a simple 1D problem and is compared with the analytical solution and other control methods. 2D and 3D examples are compared with the finite-element method. Zero-energy modes are shown to be completely damped in all cases. The computation efficiency of the explicit stress-point based peridynamic model is analyzed in the end.