The Boundary Element Method for Ordinary State-Based Peridynamics  

作　　者：Xue Liang Linjuan Wang 

机构地区：[1]State Key Laboratory for Turbulence and Complex Systems,Department of Mechanics and Engineering Science,College of Engineering,Peking University,Beijing,100871,China [2]CAPT-HEDPS,and IFSA Collaborative Innovation Center of MoE,College of Engineering,Peking University,Beijing,100871,China [3]School of Astronautics,Beihang University,Beijing,100191,China

出　　处：《Computer Modeling in Engineering & Sciences》2024年第6期2807-2834,共28页工程与科学中的计算机建模（英文）

基　　金：supported by the National Key R&D Program of China(2020YFA0710500).

摘　　要：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 particlemethod(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 propagationmodel embeddedwithin the framework ofOSPD-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,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

关 键 词：Ordinary state-based peridynamics boundary element method crack propagation fracture toughness 

分 类 号：O17[理学—数学] TP3[理学—基础数学]