Understanding the response of solid materials to shock loading is important for mitigating shock-induced damages and failures, as well as advancing the beneficial use of shock waves for material modifications. In this paper, we consider a representative brittle material, BegoStone, in the form of cylindrical bodies and submerged in water. We present a computational study on the causal relationship between the prescribed shock load and the resulting elastic waves and damage in the solid material. A recently developed three-dimensional computational framework, FIVER, is employed, which couples a finite volume compressible fluid solver with a finite element structural dynamics solver through the construction and solution of local, one-dimensional fluid-solid Riemann problems. The material damage and fracture are modeled and simulated using a continuum damage mechanics model and an element erosion method. The computational model is validated in the context of shock wave lithotripsy and the results are compared with experimental data. We first show that after calibrating the growth rate of microscopic damage and the threshold for macroscopic fracture, the computational framework is capable of capturing the location and shape of the shock-induced fracture observed in a laboratory experiment. Next, we introduce a new phenomenological model of shock waveform, and present a numerical parametric study on the effects of a single shock load, in which the shock waveform, magnitude, and the size of the target material are varied. In particular, we vary the waveform gradually from one that features non-monotonic decay with a tensile phase to one that exhibits monotonic decay without a tensile phase. The result suggests that when the length of the shock pulse is comparable to that of the target material, the former waveform may induce much more significant damage than the latter one, even if the two share the same magnitude, duration, and acoustic energy.

中文翻译：

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浸没在液体中的圆柱体的冲击损伤和动态断裂

了解固体材料对冲击载荷的响应对于减轻冲击引起的损坏和故障，以及促进冲击波对材料改性的有益利用非常重要。在本文中，我们考虑一种具有代表性的脆性材料 BegoStone，它呈圆柱体形式并浸入水中。我们对规定的冲击载荷与由此产生的弹性波和固体材料损坏之间的因果关系进行了计算研究。采用了最近开发的三维计算框架 FIVER，它通过构造和求解局部一维流固黎曼问题，将有限体积可压缩流体求解器与有限元结构动力学求解器相结合。使用连续介质损伤力学模型和元素侵蚀方法对材料损伤和断裂进行建模和模拟。该计算模型在冲击波碎石术的背景下进行了验证，并将结果与​​实验数据进行了比较。我们首先表明，在校准微观损伤的增长率和宏观断裂的阈值后，计算框架能够捕捉在实验室实验中观察到的冲击诱导断裂的位置和形状。接下来，我们介绍了一种新的冲击波形现象学模型，并对单个冲击载荷的影响进行了数值参数研究，其中冲击波形、幅度和目标材料的尺寸是变化的。特别是，我们逐渐改变波形，从具有拉伸相位的非单调衰减到没有拉伸相位的单调衰减。结果表明，当冲击脉冲的长度与目标材料的长度相当时，即使两者具有相同的幅度、持续时间和声能，前一种波形也可能比后一种波形引起更显着的损坏。