Based on the theory of multiple displacement fields, the quasi-static MPM has been extended to simulate crack behavior in this paper. Compared with the existing crack simulation methods, this new method not only avoids the meshing difficulties and complex shape functions but also supports the modeling of crack growth in an arbitrary direction. The key fracture parameters, stress intensity factors, are calculated by the interaction integral method and proved accurate through the example of a cracked plate under uniaxial tension. The crack propagation is predicted with the maximum circumferential stress criterion and applied in the simulation of a compact tension test of clay. Based on this study, the proposed method is suggested as an effective scheme for modeling soil crack behaviors that are not limited to small deformation.

基于多位移场理论，本文将准静态MPM扩展为模拟裂纹行为。与现有的裂纹模拟方法相比，该新方法不仅避免了网格划分的困难和复杂的形状函数，而且还支持对任意方向的裂纹扩展进行建模。通过相互作用积分法计算出关键的断裂参数，应力强度因子，并通过单轴拉伸下的裂纹板实例证明了其准确性。用最大圆周应力准则预测裂纹扩展，并将其应用于粘土的致密拉伸试验的模拟中。基于这项研究，该方法被建议作为一种模拟土壤裂缝行为的有效方案，该行为不仅限于小变形。