Improved method for zero-energy mode suppression in peridynamic correspondence model

Abstract

The peridynamic correspondence model provides a general formulation to incorporate the classical local model and, therefore, helps to solve mechanical problems with discontinuities easily. But it suffers from zero-energy mode instability in numerical implementation due to the approximation of deformation gradient tensor. To suppress zero-energy modes, previous stabilized methods were generally more based on adding a supplemental force state derived from bond-based peridynamic theory, which requires a bond-based peridynamic micro-modulus. In this work, we present an improved stabilized method where the stabilization force state is derived directly from the peridynamic correspondence model. Hence, the bond-based peridynamic micro-modulus is abandoned. This improved method needs no extra constant to control the magnitude of stabilization force state and it is suitable for either isotropic or anisotropic materials. Several examples are presented to demonstrate its performance in simulating crack propagation, and numerical results show its efficiency and effectiveness.