A multi-scale method based on a combination of the boundary element method (BEM) and peridynamics (PD) was developed to model crack propagation problems in two-dimensional (2D) elastic bodies. The special feature of this method is that it can take full advantage of both the BEM and PD to achieve a higher level of computational efficiency. Based on the scale of the structure and the crack location, the considered domain can be divided into non-cracked and cracked domains. The BEM is employed in the non-cracked domain, while the PD is applied in the cracked domain. This can reduce the dimension by one in the non-cracked domain for improving the modeling efficiency. A stiffness equation of the bond-based PD is established by using Taylor’s series expansion for the bond stretch and applied to simulate the cracked domain. The PD approach can automatically model the initiation and propagation of a crack. A coupling model using shared nodes is constructed by introducing the BEM nodes on the interface at the same location as the PD material points. With the continuity of displacements and equilibrium of tractions at the interface, a combined system of equations is obtained by merging the stiffness and force matrix from each domain. For test problems, the deformation and crack propagation in 2D elastic bodies subjected to quasi-static loads were analyzed. The numerical results clearly demonstrate the accuracy and efficiency of the proposed method for crack problems based on coupling the BEM and PD.

提出了一种基于边界元方法（BEM）和周边动力学（PD）相结合的多尺度方法，以对二维（2D）弹性体中的裂纹扩展问题进行建模。该方法的特殊之处在于它可以充分利用BEM和PD的优势来实现更高水平的计算效率。根据结构的规模和裂纹的位置，可以将考虑的区域分为非裂纹和裂纹区域。BEM用于非破解域，而PD用于破解域。这样可以在非破解域中将尺寸减小一倍，以提高建模效率。通过使用泰勒级数展开法对键的拉伸建立基于键的PD的刚度方程，并将其用于模拟裂纹域。PD方法可以自动模拟裂纹的萌生和扩展。通过在接口上与PD材质点相同的位置引入BEM节点，可以构造使用共享节点的耦合模型。随着界面处位移的连续性和牵引力的平衡，通过合并来自每个域的刚度和力矩阵，可以得到一个组合的方程组。对于测试问题，分析了在准静态载荷下二维弹性体内的变形和裂纹扩展。数值结果清楚地证明了基于BEM和PD耦合方法的裂纹问题的准确性和效率。通过在接口上与PD材质点相同的位置引入BEM节点，可以构造使用共享节点的耦合模型。随着界面处位移的连续性和牵引力的平衡，通过合并来自每个域的刚度和力矩阵，可以得到一个组合的方程组。对于测试问题，分析了在准静态载荷下二维弹性体内的变形和裂纹扩展。数值结果清楚地证明了基于BEM和PD耦合方法的裂纹问题的准确性和有效性。通过在接口上与PD材质点相同的位置引入BEM节点，可以构造使用共享节点的耦合模型。随着界面处位移的连续性和牵引力的平衡，通过合并来自每个域的刚度和力矩阵，可以得到一个组合的方程组。对于测试问题，分析了在准静态载荷下二维弹性体内的变形和裂纹扩展。数值结果清楚地证明了基于BEM和PD耦合方法的裂纹问题的准确性和效率。分析了二维弹性体在准静态载荷作用下的变形和裂纹扩展。数值结果清楚地证明了基于BEM和PD耦合方法的裂纹问题的准确性和效率。分析了二维弹性体在准静态载荷作用下的变形和裂纹扩展。数值结果清楚地证明了基于BEM和PD耦合方法的裂纹问题的准确性和效率。