This paper presents and validates a new local to global (L2G) FEM approach that can analyze multiple, interactive fracture processes in 2D solids with improved numerical efficiency and robustness. The method features: 1) forming local problems for individual and interactive cracks; and 2) parallel solving local problems and returning local solutions as part of the trial solution for global iteration. It has been demonstrated analytically (through a simple 1D problem) and numerically (through several benchmarking examples) that, the proposed method can substantially improve the robustness of the global solution process and significantly reduce the costly global iteration for convergence. The demonstrated improvement in numerical efficiency is up to $20\sim 40\text{\%}$ for mildly unstable problems. For problems with severely unstable crack initiation and propagation, the improvement can be more significant. This new method is readily applicable to other popular methods such as the extended FEM (X-FEM), Augmented FEM (A-FEM) and Phantom-node method (PNM).

本文介绍并验证了一种新的局部到全局 (L2G) FEM 方法，该方法可以分析二维实体中的多个交互式断裂过程，并提高数值效率和鲁棒性。该方法的特点：1）形成局部问题，针对个体和交互的裂缝；2）并行解决局部问题并返回局部解决方案作为全局迭代试验解决方案的一部分。分析（通过一个简单的一维问题）和数值（通过几个基准测试示例）已经证明，所提出的方法可以显着提高全局求解过程的鲁棒性，并显着减少代价高昂的全局迭代收敛。已证明的数值效率改进高达$20～40\text{\%}$对于轻度不稳定的问题。对于裂纹萌生和扩展严重不稳定的问题，改进可能更为显着。这种新方法很容易适用于其他流行的方法，例如扩展有限元法（X-FEM）、增强有限元法（A-FEM）和虚拟节点法（PNM）。