The Boundary Element Method for Ordinary State-Based Peridynamics

Abstract

The peridynamics (PD), as a promising nonlocal continuum mechanics theory, shines in solving discontinuous problems. Up to now, various numerical methods, such as the peridynamic mesh-free particle method (PD-MPM), peridynamic finite element method (PD-FEM), and peridynamic boundary element method (PD-BEM), have been proposed. PD-BEM, in particular, outperforms other methods by eliminating spurious boundary softening, efficiently handling infinite problems, and ensuring high computational accuracy. However, the existing PD-BEM is constructed exclusively for bond-based peridynamics (BBPD) with fixed Poisson's ratio, limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems. In this paper, we address these limitations by introducing the boundary element method (BEM) for ordinary state-based peridynamics (OSPD-BEM). Additionally, we present a crack propagation model embedded within the framework of OSPD-BEM to simulate crack propagations. To validate the effectiveness of OSPD-BEM, we conduct four numerical examples: deformation under uniaxial loading, crack initiation in a double-notched specimen, wedge-splitting test, and threepoint bending test. The results demonstrate the accuracy and efficiency of OSPD-BEM, highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson's ratios. Moreover, OSPD-BEM significantly reduces computational time and exhibits greater consistency with experimental results compared to PD-MPM.