Modeling the branching behavior of dynamic brittle crack helps reveal dynamic mechanism of brittle geomaterial fragmentation induced by multi crack bifurcation. In this study, the correlation between crack propagation speed and separation strain rate of crack surfaces is derived theoretically and verified based on the Kalthoff plate impact test, showing a strong linear positive proportional relationship. A rate-dependent constitutive law for cohesive element is proposed to predict the direction and branching of dynamic crack. The methodology of compiling the rate-dependent model for cohesive element via the user subroutine VUSDFLD is introduced. The sensitivity of element size, mesh structure, and material parameters to the dynamic branching model are discussed. Four models with different rate-dependent forms are compared with the previous numerical results to find the best one. It is found that the most superior constitutive relationship for cohesive element in modeling crack branching is the model in which only the maximum separation displacement is rate-dependent, and the traction strength keeps constant. As Young’s modulus increases, the position of the first large branching is advanced due to the increase of stress wave speed. The crack branching angle is positively correlated with fracture energy, which is speculated to be closely related to the geometrical nonlinearity of the tested plate and the redistribution of tensile stress. The appearance of fracture process zone of dynamic crack represented by the damage cohesive elements is investigated, based on which the branching mechanism and the number of crack branches are discussed. Unlike static crack, the fracture process zone of dynamic crack represented by the damage cohesive element zone shows a fan shape, of which the radius is also rate-dependent. The extent of the dynamic fracture process zone varies with the crack propagation speed, which controls the generation of subsequent crack branches and the instability of crack direction.

对动态脆性裂纹的分支行为进行建模有助于揭示多裂纹分叉引起的脆性岩土碎裂的动力学机制。本研究从理论上推导了裂纹扩展速度与裂纹表面分离应变率之间的相关性，并基于Kalthoff板冲击试验对其进行了验证，结果显示出很强的线性正比例关系。提出了一种基于速率的粘结单元本构律，用于预测动态裂纹的方向和分支。介绍了通过用户子程序VUSDFLD编译速率依赖模型的内聚元素的方法。讨论了单元尺寸，网格结构和材料参数对动态分支模型的敏感性。将四种具有不同速率依赖形式的模型与以前的数值结果进行比较，以找到最佳模型。结果表明，在裂纹分支建模中，粘性元件最优越的本构关系是仅最大分离位移与速率相关且牵引强度保持恒定的模型。随着杨氏模量的增加，第一大分支的位置由于应力波速度的增加而前进。裂纹分支角与断裂能呈正相关，推测与断裂能与被测板的几何非线性和拉应力的重新分布密切相关。研究了以损伤内聚力为代表的动态裂纹断裂过程区的出现，在此基础上，讨论了裂纹的分支机理和裂纹分支的数量。与静态裂纹不同，动态裂纹的断裂过程区域以损伤内聚元素区域为代表，呈扇形，其半径也与速率有关。动态断裂过程区的范围随裂纹扩展速度的变化而变化，从而控制后续裂纹分支的产生和裂纹方向的不稳定性。