Abstract Applying parameter mapping theory, this paper establishes a new three dimension lattice-spring model (3D-LSM) containing the rotational degree of freedom. Using the finite element method (FEM) and share grid, the spring stiffness coefficient is obtained with a rigorous mathematical logic. This 3D-LSM contains the nearest neighbor, next nearest neighbor and third nearest neighbor which highly increases the accuracy of the system. Wave velocity in elastic solid and dynamic fracture of concrete l -specimen are calculated by both 3D-LSM and elastic theory. Results indicate that this model can present the behavior of the material in the elastic stage. By introducing the energy balance principle, 3D-LSM can simulate dynamic brittle fracture both in mesoscopy and macroscopy. This model is used to analyze the evolution law of crack propagation path and propagation velocity in brittle materials under dynamic tension of shock wave. The results show that the stress concentration area at the crack tip changes during the crack propagation, showing a "butterfly shape" before the crack initiation and a "swept wing shape" after the crack initiation. After the crack initiation, the crack tip velocity jumps instantly and then increases continuously, corresponding to the expansion of a single crack. Then the tip velocity decreases slightly and increases to the maximum crack propagation velocity, corresponding to the crushing stage before bifurcation. After that, the crack growth rate will oscillate significantly, which corresponds to the bifurcation stage of the crack.

中文翻译：

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具有旋转自由度的三维晶格弹簧模型及其在裂纹动态扩展中的应用

摘要 应用参数映射理论，建立了一种新的包含旋转自由度的三维晶格弹簧模型(3D-LSM)。使用有限元法（FEM）和共享网格，通过严格的数学逻辑获得弹簧刚度系数。这个 3D-LSM 包含最近邻、次近邻和第三近邻，这大大提高了系统的准确性。弹性固体中的波速和混凝土 l 试样的动态断裂是通过 3D-LSM 和弹性理论计算的。结果表明，该模型可以呈现材料在弹性阶段的行为。通过引入能量平衡原理，3D-LSM 可以在介观和宏观上模拟动态脆性断裂。该模型用于分析冲击波动态张力下脆性材料裂纹扩展路径和扩展速度的演化规律。结果表明，裂纹扩展过程中裂纹尖端应力集中面积发生变化，裂纹萌生前呈现“蝴蝶形”，裂纹萌生后呈现“后掠翼形”。裂纹萌生后，裂纹尖端速度瞬间跳跃，然后不断增大，对应于单个裂纹的扩展。然后尖端速度略有下降并增加到最大裂纹扩展速度，对应于分叉前的破碎阶段。之后，裂纹扩展速率将出现显着振荡，对应于裂纹的分叉阶段。