Convergence study of stabilized non-ordinary state-based peridynamics for elastic and fracture problems

Abstract

Non-ordinary state-based peridynamics simulates crack propagation while avoiding the imposition of additional criteria to describe the responses at discontinuities. However, an incomplete coverage by the sphere of a horizon near the boundaries and crack surfaces could cause the boundary effect. In this study, the boundary effects occurring in the stress concentration region are investigated in δ- and m-convergence tests for elastic deformation and crack propagation. Three types of boundary imposition methods are investigated in m-convergence and the method showing the fastest convergence is applied to fracture problems. The weighted average stress estimation is proposed for the damage criterion to reduce the variation in the crack paths in the convergence test, and the weight function is defined as a parameter that can change the shape of the function into three different forms: linear, bilinear, and constant. The fracture simulation is performed in an L-shaped panel with varying geometrical parameters. As a result, the bilinear weighted average stress estimation reduces the variation in the crack path compared to the conventional arithmetic average estimation method. Therefore, the proposed weighted average stress estimation method increases the accuracy of the crack path prediction and will enlarge the application area for fracture simulation using peridynamics.