Dynamic photoelastic studies of wave propagation in granular media

The optical method of dynamic photoelasticity is used to visualize the load transfer profiles due to explosive loading in granular aggregates. The granular media are simulated by using arrays of disks fabricated from a brittle polyester material—Homalite 100. Attention is focused on the effect of microstructure or the geometrical packing of the grains on the wave propagation phenomena. The experimental data are analyzed to obtain the stress wave attenuation, wave velocities and contact stresses as a function of time along various directions in the assembly of grains. Dynamic load transfer functions are developed to predict dynamic contact loads in any systematic or random assembly of grains for any given loading. The predicted results are compared with the experimental data. The effect of local inhomogeneities on the wave propagation phenomena is also shown.     

瞬态波位移场计算方法在相控阵声场模拟中的实验验证

通过实验研究了声束偏转不同角度和声场半径变化时线性相控阵的声场特性,并与基于瞬态波位移解析解的相控阵声场计算方法得到的理论结果进行了对比。首先研究了基于半圆圆弧离面瞬态位移的声场计算方法,并进行了数值计算可靠性的优化。然后建立了一套相控阵瞬态波位移场的测量系统,以半圆形钢板为试件,纵波传感器为接收传感器,测量了偏转角度为-10°,-30°,-50°,-70°,及声场半径为50 mm,75 mm,100 mm和125 mm时线性超声相控阵的声束指向性;同时以基于瞬态波位移解析解的相控阵声场计算方法,计算了相同条件下该相控阵的声束指向性。最后将实验结果与理论结果进行了对比,取得了较好的一致。说明基于瞬态波位移的相控阵声场计算方法可以较好地计算线阵的声场,对于声束偏转较大角度和声场半径变化时也同样有效。     

Modeling elastic wave propagation in kidney stones with application to shock wave lithotripsy

A time-domain finite-difference solution to the equations of linear elasticity was used to model the propagation of lithotripsy waves in kidney stones. The model was used to determine the loading on the stone (principal stresses and strains and maximum shear stresses and strains) due to the impact of lithotripsy shock waves. The simulations show that the peak loading induced in kidney stones is generated by constructive interference from shear waves launched from the outer edge of the stone with other waves in the stone. Notably the shear wave induced loads were significantly larger than the loads generated by the classic Hopkinson or spall effect. For simulations where the diameter of the focal spot of the lithotripter was smaller than that of the stone the loading decreased by more than 50%. The constructive interference was also sensitive to shock rise time and it was found that the peak tensile stress reduced by 30% as rise time increased from 25 to 150 ns. These results demonstrate that shear waves likely play a critical role in stone comminution and that lithotripters with large focal widths and short rise times should be effective at generating high stresses inside kidney stones.     

Structure of the phase transition zone in solids induced by a shock wave

The problem of a strong shock wave inducing a phase transition in a solid medium is considered. It is assumed that the solid medium transforms from a low pressure phase to a high pressure phase. A relation between the density of the medium and the function of advancement of the transition is obtained. The behaviour of some other thermodynamical parameters in the transition zone is found. All the equations are expressed in terms of dimensionless quantities and are then valid for a wide range of materials. Some particular examples as well as numerical results are presented.     

The role of energy density and acoustic cavitation in shock wave lithotripsy

Today a high percentage of urinary stones are successfully treated by extracorporeal shockwave lithotripsy (SWL); however, misconceptions regarding fragmentation mechanisms, as well as treatment parameters like dose, applied energy and focal area are still common. A main stone comminution mechanism during SWL is acoustic cavitation. The objective of this study was to analyze the influence of cavitation and energy density on stone fragmentation. A research lithotripter was used to expose a large set of artificial kidney stones to shock waves varying different parameters. Hundreds of pressure records were used to calculate the energy density of the lithotripter at different settings. Results indicate that energy density is a crucial parameter and that better SWL treatment outcomes could be obtained placing the calculus at a prefocal position.     

Modified shock waves for extracorporeal shock wave lithotripsy: a simulation based on the Gilmore formulation

Extracorporeal shock wave lithotripsy (SWL) is a reliable therapy for the treatment of urolithiasis. Nevertheless, improvements to enhance stone fragmentation and reduce tissue damage are still needed. During SWL, cavitation is one of the most important stone fragmentation mechanisms. Bubbles with a diameter between about 7 and 55 μm have been reported to expand and collapse after shock wave passage, forming liquid microjets at velocities of up to 400 m/s that contribute to the pulverization of renal calculi. Several authors have reported that the fragmentation efficiency may be improved by using tandem shock waves. Tandem SWL is based on the fact that the collapse of a bubble can be intensified if a second shock wave arrives tenths or even a few hundredths of microseconds before its collapse. The object of this study is to determine if tandem pulses consisting of a conventional shock wave (estimated rise time between 1 and 20 ns), followed by a slower second pressure profile (0.8 μs rise time), have advantages over conventional tandem SWL. The Gilmore equation was used to simulate the influence of the modified pressure field on the dynamics of a single bubble immersed in water and compare the results with the behavior of the same bubble subjected to tandem shock waves. The influence of the delay between pulses on the dynamics of the collapsing bubble was also studied for both conventional and modified tandem waves. For a bubble of 0.07 mm, our results indicate that the modified pressure profile enhances cavitation compared to conventional tandem waves at a wide range of delays (10-280 μs). According to this, the proposed pressure profile could be more efficient for SWL than conventional tandem shock waves. Similar results were obtained for a ten times smaller bubble.     

The use of resonant scattering to identify stone fracture in shock wave lithotripsy

There is currently little feedback as to whether kidney stones have fractured during shock wave lithotripsy. Resonant scattering of the lithotripter shock wave was used here to differentiate intact and fractured stone models in water. Scattering, including reflection and radiation due to reverberation from within the stone, was calculated numerically with linear elasticity theory and agreed well with measurements made with a focused receiver. Identification of fracture was possible through frequency analysis, where scatter from fractured stones was characterized by higher energy in distinct bands. High-speed photography concurrent with measurement indicated the effect was not due to cavitation.     

超声聚焦探头在固体中辐射声场的动态光弹测量方法

超声聚焦探头在声场聚焦区域具有很高的检测灵敏度和分辨力,是工业超声检测中常用的探头。聚焦探头在固体中的聚焦特性直接影响检测效果,其传统测量方法通过水中聚焦参数间接换算而来,结果存在一定的误差。动态光弹法可以直接观测透明固体中的探头辐射声场,具有直观、无反射体或水听器的浸入影响、全场观测等特征。进一步采用圆偏振光并结合Senarmont补偿法,可精确测量透明固体中探头辐射声场的绝对应力分布,给出聚焦探头在固体中的聚焦参数,包括焦距、焦柱长度和焦斑宽度。实验测量结果与有限元仿真计算及小球反射法测量结果吻合较好,表明了动态光弹法定量测量聚焦探头辐射声场的可行性。     

Bubble proliferation in the cavitation field of a shock wave lithotripter

Lithotripter shock waves (SWs) generated in non-degassed water at 0.5 and 2 Hz pulse repetition frequency (PRF) were characterized using a fiber-optic hydrophone. High-speed imaging captured the inertial growth-collapse-rebound cycle of cavitation bubbles, and continuous recording with a 60 fps camcorder was used to track bubble proliferation over successive SWs. Microbubbles that seeded the generation of bubble clouds formed by the breakup of cavitation jets and by bubble collapse following rebound. Microbubbles that persisted long enough served as cavitation nuclei for subsequent SWs, as such bubble clouds were enhanced at fast PRF. Visual tracking suggests that bubble clouds can originate from single bubbles.     

激光驱动的冲击波自生磁场以及外加磁场的冲击波放大研究

冲击波是天体物理观测中常见的现象, 其对粒子的加速被认为是高能宇宙射线的来源. 宇宙中冲击波周围往往存在很强的磁场, 但人们对于此类强磁场的产生放大过程的理解并不充分. 本文利用二维粒子模拟程序研究了激光与磁化或者非磁化等离子体相互作用产生的冲击波现象, 给出了冲击波波前处磁场的产生放大特性. 研究发现, 作用过程中的自生磁场可以储存能量, 从而进一步加速电子; 当存在外加磁场时, 由冲击波加速的电子和离子的能量都比同条件下非磁化等离子体的能量高; 而且外加磁场藉由冲击波放大倍数则与其值有极大关系. 与天文观测中推断的磁场与背景磁场相比放大千倍这一研究结果的比较可以看出, 天体冲击波周围磁场放大主要是由局域内生磁场导致的.     

On wave radiation induced by a fast shock wave in an oblique magnetic field

The corrugation stability of the flat surface of a fast magnetohydrodynamic shock wave in a perfect monoatomic gas with a constant heat capacity is studied with numerical techniques. The magnetic field makes an arbitrary angle with the plane of discontinuity. It is shown that the shock wave remains stable only if it is strictly perpendicular to the magnetic field. At any other angle between the fast shock wave and magnetic field, the former may spontaneously radiate outwardly propagating magnetohydrodynamic waves under certain conditions. Incoming flow characteristics at which these waves are induced are determined.     

Multi-scale method study of nano-void under the shock wave

The dynamic behavior of nano-void in metal Al under shock loading is simulated by using the multi-scale numerical simulation method. This method couples the molecular dynamics method used in local defect domain and the finite element method overall domain. The macroscopic failure of material is analyzed based on the microscopic dynamic behavior of nano-void. Our results show that the collapse of nano-void depends on the shock strength. Both a high and a low stress region are formed in the region of void after void collapse, whereas only a low stress region is formed under no collapse. The local hot spot is displayed in the temperature field, and a detailed analysis reveals that the hot point initiation is caused by recompression of atoms in void.     

Simulations of shock waves in solids

Molecular dynamic shock wave simulations have been carried out for face centered cubic (f.c.c.) and body centered cubic (b.c.c.) solids using Lennard-Jones and Morse potentials for the interatomic interactions. The Hugoniot conservation relations were accurately obeyed in all of these calculations. The shock wave profiles may vary with the interatomic potential and the crystal structure, effects most clearly shown by the temperature profile near the shock front. The Lennard-Jones solids are intensitive to a change in structure but the Morse solids appear sensitive to crystal structure, at least in comparing b.c.c. with f.c.c. It was shown that the average shock wave temperature can be calculated from a combination of the Hugoniot conservation relations and the Mie-Grüneisen equation of state. The temperature calculated this way is in good agreement with the average shock wave temperature obtained in the computer simulations.     

Spin-diffusion NMR at low field for the study of multiphase solids

The use of spin-diffusion NMR for the measurement of domain sizes in multiphase materials is becoming increasingly popular, in particular for the study of heterogeneous polymers. Under conditions where T(1) relaxation can be neglected, which is mostly the case at high field, analytical and approximate solutions to the evolution of spin diffusion are available. In order to extend the technique to more general conditions, we performed a comprehensive study of the diffusion of magnetization in a model copolymer at low field, where T(1) tends to be of the same order of magnitude as the typical spin-diffusion time. In order to study the effects of T(1) and to delineate the optimal T(1) values for back correction prior to applying the initial-rate approximation, we developed a numerical simulation based on the diffusion equation and including longitudinal relaxation. We present and discuss the limits of simple correction strategies for initial-slope analysis based on apparent relaxation times from saturation-recovery experiments or the spin-diffusion experiments themselves. Our best strategy faithfully reproduces domain sizes obtained by both TEM investigations and full simultaneous fitting of spin-diffusion and saturation-recovery curves. Full fitting of such independent data sets not only yields correct domain sizes, but also the true longitudinal relaxation times, as well as spin-diffusion coefficients. Effects of interphases with distinct mobility on spin-diffusion curves, as well as practical hints concerning the reliable component decomposition of the detected low-resolution FID signal by help of different magnetization filters are also discussed in detail.     

固体中脉冲激光激发声表面波的理论研究

本文运用本征函数展开的方法对固体材料中脉冲激光激发的声表面波进行了理论研究，在考虑热弹激发的条件下，利用三维的轴对称模型，得到了脉冲激光光源的脉冲宽度以及聚焦半径对固体材料中声表面波信号的时域及频域的影响，对进行超短脉冲激光激发超声的研究具有指导意义。     

激光引致激波演化数值研究

在高重复频率激光推进的研究中,激波的合并是发生在激波演化后期的,同时由于脉冲间隔短,脉冲宽度对流场演化的影响也需要详细研究。考虑了激光辐照过程对流场演化的影响,通过数值计算对激波演化特性进行了研究。结果表明,初期波阵面的椭球形状逐渐转化为一个球形,球心与击穿点的距离随时间逐渐减小并最终趋于稳定。基于激波合并的应用,当激波马赫数在1~2之间时,给出了激波波阵面半径随时间的变化规律,以及激波高压区长度和波峰压强随激波波阵面半径变化规律的经验公式。     

Measurement of shock heating in laser-irradiated solids

We have obtained the first temporally resolved measurement of the entire visible spectrum of shock-induced luminescence from the rear surface of a laser-irradiated aluminum foil. This yielded a detailed time history (200 ps resolution) of the spectral temperature of the target rear surface. The results were consistent with that obtained from brightness temperature measurements. The measured shock-heated temperature also showed good agreement with hydrodynamic simulations addressing the effect of shock-unloading in the target rear side.     

New approaches to the full-field analysis of photoelastic stress patterns

This paper presents two new methods that provide a complete solution for the automatic fringe analysis of photoelastic data. Previous solutions have not yet provided a complete full-field analysis of both fringe sets (isochromatic and isoclinic) over a multiple number of fringes with an automatic measurement of absolute magnitude. This paper reviews previous approaches and discusses the options along which this work has been directed. Specifically, two new algorithms are presented. Firstly, the combination of phase maps at three wavelengths in order to remove the isochromatic ambiguity at every π turning point, that would occur in a single phase map. Additionally, this algorithm allows the automatic measurement of absolute magnitude, providing the neutral axis is within the field of view. Secondly, a new method is proposed that removes the areas of 2π ambiguity in an isoclinic phase map by cross-correlating regions of low modulation at two different wavelengths. The algorithms are demonstrated by applying them to the analysis of an engine connecting rod. The rod was manufactured as a full-scale three-dimensional model in araldite (Ciba-Geigy CT200), from which a central slice was taken after having been stress frozen.