A novel method for predicting dynamic crack propagation based on coupling the boundary element method (BEM) and bond-based peridynamics (BBPD) is developed in this work. The special feature of this method is that it can take full advantages of both the BEM and PD to achieve a higher level of accuracy and efficiency. Based on the scale of the structure and the location of cracks, the considered domain can be divided into a non-cracked region and a cracked region. For the non-cracked region, a meshfree boundary-domain integral equation method (meshfree-BDIEM) is employed in the analysis to reduce the dimension by one and to increase the computational efficiency. The bond-based PD is applied to simulate the cracked region, which can model the initiation and propagation of the cracks automatically. The boundary nodes from the BEM on the interfaces can interact with the material points from the PD directly. By using the displacement continuity and force equilibrium conditions on the interfaces, a combined model is obtained by merging the mass, stiffness, and force matrices from each region of the domain. Both the implicit and explicit BEM-PD coupled solution methods can deliver accurate results without inducing the ghost forces. Several benchmark problems of dynamic crack propagation have been modeled by using the method, which demonstrate that the developed BEM-PD coupled approach can be an efficient numerical tool to model the dynamic crack propagation problems.

本文开发了一种基于耦合边界元法(BEM) 和基于键的近场动力学 (BBPD)预测动态裂纹扩展的新方法。该方法的特殊之处在于它可以充分利用边界元法和局部放电法，从而达到更高水平的精度和效率。根据结构的规模和裂纹的位置，所考虑的区域可以分为非裂纹区域和裂纹区域。对于非开裂区域，采用无网格边界域积分方程法（meshfree-BDIEM）进行分析，降维一维，提高计算效率。应用基于键的 PD 模拟裂纹区域，可以自动模拟裂纹的萌生和扩展。这界面上 BEM 的边界节点可以直接与 PD 的材料点交互。通过使用界面上的位移连续性和力平衡条件，通过合并域中每个区域的质量、刚度和力矩阵来获得组合模型。隐式和显式 BEM-PD 耦合求解方法都可以提供准确的结果，而不会产生鬼力。使用该方法对动态裂纹扩展的几个基准问题进行了建模，这表明所开发的 BEM-PD 耦合方法可以成为模拟动态裂纹扩展问题的有效数值工具。