Specific conditions at the tip of a crack and discontinuities in a material are the challenges in analyzing the growth of cracks using conventional methods. In recent years, a method has been developed based on the non-local mechanics, called peridynamic theory, which has improved the analysis process of such structures. In this theory, the points of matter whose displacement or displacement derivatives are discontinuous are not distinguished from other material points. In this paper, we employed the bond-based peridynamic theory to investigate the rate of crack propagation and the path of crack growth in a beam with an initial crack due to low velocity impact. Two beams made of polymethyl-methacrylate (PMMA) and steel alloy with different projectile shapes were considered. The effects of changes in the impact velocity and the fracture toughness were studied and the obtained results were validated with other conducted studies. The crack path was predicted successfully and the branching of the crack was captured. The results confirm the ability of the peridynamic theory to model the crack growth in impact problems.

裂纹尖端的特定条件和材料的不连续性是使用常规方法分析裂纹扩展的挑战。近年来，基于非局部力学的方法被开发出来，被称为周动力理论，它改善了这种结构的分析过程。在该理论中，位移或位移导数不连续的物质点与其他物质点没有区别。在本文中，我们采用基于键的绕动力学理论研究了低速冲击引起的具有初始裂纹的梁的裂纹扩展速率和裂纹扩展路径。考虑了由聚甲基丙烯酸甲酯（PMMA）和钢合金制成的具有不同弹丸形状的两根梁。研究了冲击速度和断裂韧度变化的影响，并用其他进行的研究验证了所得结果。成功预测了裂纹路径并捕获了裂纹的分支。结果证实了围力学理论对冲击问题中裂纹扩展进行建模的能力。