A discrete surface correction method for bond-based peridynamics

Abstract

The peridynamic (PD) material parameters at boundaries where the neighborhood is incomplete exhibit a softer material response compared to bulk material points. This effect is called the surface or skin effect. This study presents a new surface correction method for bond-based peridynamics that calculates the PD material parameters discretely during numerical simulations. The discretely calculated material parameters can easily account for the effect of newly formed free surfaces, i.e., crack surfaces, that can occur during the simulation. Hence, the proposed surface correction technique provides a single context for a surface correction method that can be applied to static problems and dynamic problems. In numerical simulations, the meshfree discretization technique enhanced with the HHB algorithm is utilized for the spatial discretization to improve accuracy in the numerical integration over the spatial domain. In addition, a half-step time integration scheme is used in temporal discretization. The results obtained using the proposed surface correction method are compared with the surface correction methods available in the literature. It is shown that the proposed surface correction method is more accurate in the static and dynamic PD analyses by considering the missing neighbors along the problem boundaries and the newly emerging boundaries during the crack propagation.