S. Cao et al., 2019: Shock-Induced Damage and Dynamic Fracture in Cylindrical Bodies Submerged in Liquid
Cao S, Zhang Y, Liao D, Zhong P, Wang KG.
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States.
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 90271, United States
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.
Int J Solids Struct. 2019 Sep;169:55-71. doi: 10.1016/j.ijsolstr.2019.04.002. Epub 2019 Apr 2. FREE ARTICLE
This is another paper investigating the mechanism of fragmentation of brittle material, such as kidney stones, by shock waves. Understanding fracture dynamics and the mechanism of tissue lesions may help to develop better and safer lithotripters. The authors develop and apply a sophisticated mechanical damage model and test it against experimental data. Since unregularly shapes and complex constituents of natural kidney stones complicate computational analysis, they used cylindrical specimen with clear boundary conditions made of BegoStone material to simulate lithotripsy procedures. To gain basic understanding of a fracture model the effect of single shocks are calculated although real lithotripsy treatments require multiple shocks up to several hundred or thousands.
Three remarkable findings could be evaluated:
1. Planar cracks at the distal end of the specimens could be computed and verified in repeated experiments. The cracks seem to be similar to those created by Hopkinson’s effect.
2. The tensile part of a lithotripter shockwave can enhance fragmentation efficiency. This is remarkable since usually tensile pressures are made responsible only for cavitation.
3. Smaller specimen require more shock doses to break.
Calculations and experiments presented in this paper are based, as usual, on clearly defined conditions of cylindrical specimen of known composition. Real kidney stones however are too complex to be analysed by the presented computational model.
The reported results well correspond with findings achieved in another paper (1) offering an alternative fracture mechanism. Different from usual approaches, momentum transfer is considered an important mechanism of fragmentation. So far, the momentum of a shock wave was payed little attention. Viewing the problem of fragmentation by momentum transfer can provide explication of all three points listed above including Hopkinson’s effect of spallation and does not necessarily require regularly shaped specimen.
Fragmentation of brittle material by shock wave lithotripsy.
Momentum transfer and inertia: a novel view on fragmentation
Wess O, Mayer J.