Acoustic virtual mass of granular media

Mechanical coupling between grains in a randomly packed unconsolidated granular medium is shown to cause an increase in the effective inertia, hence, a reduction in sound and shear wave speeds, relative to predictions by the standard expressions for a uniform elastic solid. The effect may be represented as a virtual mass term, and directly related to the scintillation index of the grain-to-grain contact stiffness.     

Acoustoelasticity in soft solids: assessment of the nonlinear shear modulus with the acoustic radiation force

The assessment of viscoelastic properties of soft tissues is enjoying a growing interest in the field of medical imaging as pathologies are often correlated with a local change of stiffness. To date, advanced techniques in that field have been concentrating on the estimation of the second order elastic modulus (mu). In this paper, the nonlinear behavior of quasi-incompressible soft solids is investigated using the supersonic shear imaging technique based on the remote generation of polarized plane shear waves in tissues induced by the acoustic radiation force. Applying a theoretical approach of the strain energy in soft solid [Hamilton et al., J. Acoust. Soc. Am. 116, 41-44 (2004)], it is shown that the well-known acoustoelasticity experiment allowing the recovery of higher order elastic moduli can be greatly simplified. Experimentally, it requires measurements of the local speed of polarized plane shear waves in a statically and uniaxially stressed isotropic medium. These shear wave speed estimates are obtained by imaging the shear wave propagation in soft media with an ultrafast echographic scanner. In this situation, the uniaxial static stress induces anisotropy due to the nonlinear effects and results in a change of shear wave speed. Then the third order elastic modulus (A) is measured in agar-gelatin-based phantoms and polyvinyl alcohol based phantoms.     

Sonoelastographic imaging of interference patterns for estimation of shear velocity distribution in biomaterials

The authors have recently demonstrated the shear wave interference patterns created by two coherent vibration sources imaged with the vibration sonoelastography technique. If the two sources vibrate at slightly different frequencies omega and omega+deltaomega, respectively, the interference patterns move at an apparent velocity of (deltaomega/2omega)upsilon(shear), where upsilon(shear) is the shear wave speed. We name the moving interference patterns "crawling waves." In this paper, we extend the techniques to inspect biomaterials with nonuniform stiffness distributions. A relationship between the local crawling wave speed and the local shear wave velocity is derived. In addition, a modified technique is proposed whereby only one shear wave source propagates shear waves into the medium at the frequency omega. The ultrasound probe is externally vibrated at the frequency omega-deltaomega. The resulting field estimated by the ultrasound (US) scanner is proven to be an exact representation of the propagating shear wave field. The authors name the apparent wave motion "holography waves." Real-time video sequences of both types of waves are acquired on various inhomogeneous elastic media. The distribution of the crawling/holographic wave speeds are estimated. The estimated wave speeds correlate with the stiffness distributions.     

Nonlinear waves in dry and wet Hertzian granular chains

A one-dimensional dry granular medium, a chain of beads which interact via the nonlinear Hertz potential, exhibits strongly nonlinear behaviors. When such an alignment further contains some fluid in the interstices between grains, it may exhibit new interesting features. We report some recent experiments, analysis and numerical simulations concerning nonlinear wave propagation in dry and wet chains of spheres. We consider first a monodisperse chain as a reference case. We then analyze how the pulse characteristics are modified in the presence of an interstitial viscous fluid. The fluid not only induces dissipation but also strongly affect the intergrain stiffness: in a wet chain, wave speed is enhanced and pulses are shorter. Simple experiments performed with a single sphere colliding a wall covered by a thin film of fluid confirm these observations. We demonstrate that even a very small amount of fluid can overcome the Hertzian potential and is responsible for a large increase of contact stiffness. Possible mechanisms for wet contact hardening are related to large fluid shear rate during fast elastohydrodynamic collision between grains.     

Interaction of acoustic waves with polycrystals

We analyze theoretically the structure of the field created in a semi-infinite polycrystal by an acoustic wave, coming from an isotropic homogeneous medium and incident normally onto its surface. The elastic anisotropy of the polycrystal is supposed to be small, and the perturbation theory is applied. It is shown that the effective medium approach is not valid. In addition to the transmitted wave propagating in the polycrystal with an effective sound speed, there is one more bulk wave, whose amplitude decreases at a distance of the order of the mean size of the grain from the interface. The structure of the reflected wave is the same as when reflecting from an isotropic solid. However, the relation between the amplitudes of reflected and transmitted waves differs from that in an isotropic solid.     

Quantifying elasticity and viscosity from measurement of shear wave speed dispersion

The propagation speed of shear waves is related to frequency and the complex stiffness (shear elasticity and viscosity) of the medium. A method is presented to solve for shear elasticity and viscosity of a homogeneous medium by measuring shear wave speed dispersion. Harmonic radiation force, introduced by modulating the energy density of incident ultrasound, is used to generate cylindrical shear waves of various frequencies in a homogeneous medium. The speed of shear waves is measured from phase shift detected over the distance propagated. Measurements of shear wave speed at multiple frequencies are fit with the theoretical model to solve for the complex stiffness of the medium. Experiments in gelatin phantoms show promising results validated by an independent method. Practical considerations and challenges in possible medical applications are discussed.     

Resonant ultrasound spectroscopy and homogeneity in polycrystals

Resonant ultrasound spectroscopy (RUS) is capable of determining the bulk elastic properties of a solid from its characteristic vibration frequencies, given the dimensions, density and shape of the sample. The model used for extracting values of the elastic constants assumes perfect homogeneity, which can be approximated by average-isotropic polycrystals. This approximation is excellent in the small grain regime assumed for most averaging procedures, but for real samples with indeterminate grain size distributions, it is not clear where the approximation breaks down. RUS measurements were made on pure copper samples where the grain size distribution was changed by progressive heat treatments in order to find a quantitative limit for the loss of homogeneity. It is found that when a measure of the largest grains is 15% of the sample’s smallest dimension, the deviation in RUS fits indicates elastic inhomogeneity.     

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.     

颗粒样品形变对声波传播影响的实验探究

为了更好地理解颗粒间接触结构的变化对通过颗粒介质中的声波的影响,本文利用单轴压缩实验,通过一系列增加的轴向压力使样品塑性应变不断增大,这在颗粒尺度上对应于颗粒间接触结构的改变.我们测量了此过程中通过颗粒样品的声波变化,结果表明颗粒体系内接触结构的变化对声波波形中的非相干波部分和频率有明显的影响,并且在样品接触结构变化的初始阶段声速是偏离有效介质理论的预测的.     

海底沉积物压缩波速度与切变波速度的关系

基于连续介质假设,根据无吸收各向同性弹性介质通用方程分析沉积物声波传播关系,提出应用弹性结构分布因子表达的声速通用模型(GMSS,General Model of Sound Speed)分析海底沉积物的声速特性;通过研究Willey时间平均模型、Wood方程、Gassmann方程、Buckingham模型、Biot-Stoll模型和EDFM模型,可以表述成GMSS通用模型中的弹性结构分布因子的具体表达形式,得出GMSS通用模型在解释压缩波速度和切变波速度特性上具有一致性的特点。GMSS通用模型具有弹性结构分布因子、孔隙度、孔隙海水的等效密度和等效弹性模量、固相颗粒的等效密度、固相颗粒的等效体积弹性模量和等效切变弹性模量共7个参数,为研究海底沉积物压缩波和切变波速度提供了一种模型简单、参数少、通用性强的方法。但也需要从物理结构上以及应力应变关系上开展更为深入的分析和探寻GMSS模型的物理意义和参数测量的方法。      

磁性颗粒膜法拉第转角的研究

在外磁场作用下,复合介质的法拉第磁光效应依赖于颗粒膜电介质张量。而复合介质的电介质张量的计算相当复杂。运用了有效介质近似理论,利用非均匀复合介质的有效电场等于单个颗粒中局域场的平均值的自恰条件,由电介质张量εe方程及自洽条件导出了计算磁性颗粒膜系统磁光法拉第转角的解析公式。并应用导出的关系,以Cu金属颗粒为例,讨论了颗粒膜中金属颗粒含量及对应的基质、离子浓度、颗粒形状对法拉第转角的影响,结果表明,利用有效介质近似理论计算的结果与实验结果一致。     

Strain localisation in granular media

This paper discusses strain localisation in granular media by presenting experimental, full-field analysis of mechanical tests on sand, both at a continuum level, as well as at the grain scale. At the continuum level, the development of structures of localised strain can be studied. Even at this scale, the characteristic size of the phenomena observed is in the order of a few grains. In the second part of this paper, therefore, the development of shear bands within specimen of different sands is studied at the level of the individual grains, measuring grains kinematics with x-ray tomography. The link between grain angularity and grain rotation within shear bands is shown, allowing a grain-scale explanation of the difference in macroscopic residual stresses for materials with different grain shapes. Finally, rarely described precursors of localisation, emerging well before the stress peak are observed and commented.     

颗粒介质中的粘滞系数

将颗粒介质看成是等效均匀介质, 其中的声衰减系数和声速等于该颗粒介质中的相应的量值(它们可由作者的理论给出), 等效静态密度可以用二元混合规则求得. 此外, 根据浓颗粒介质中相互作用的声传播理论, 当入射波为平面波时, 相互作用的次级波仍然是平面波. 在这样的情况下, 可以将三维非线性方程组简化为一维情况, 从而算得浓颗粒介质中的粘滞系数, 结果表明, 颗粒介质中的粘滞系数不仅依赖于颗粒的体积分数而且还与频率有关. 根据推导过程可知, 对比于爱因斯坦理论所能应用的限制, 本文的结果可以更广泛地应用于实际介质.     

Stationary shear flows of dense granular materials: a tentative continuum modelling

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent qualitative agreement with most of the experimental or numerical results concerning free-surface shear flows as well as confined shear flows.Received: 24 March 2004, Published online: 29 June 2004PACS: 45.70.Ht Avalanches - 45.70.-n Granular systems - 83.80.Fg Granular solids     

Slow granular flows: The dominant role of tiny fluctuations

What mechanism governs slow flows of granular media? Microscopically, the grains experience enduring frictional contacts in these flows. However, a straightforward translation to a macroscopic frictional rheology, where the shear stresses are proportional to the normal stresses with a rate-independent friction coefficient, fails to capture important aspects of slow granular flows. There is now overwhelming evidence that agitations, tiny fluctuations of the grain positions, associated with large fluctuation of their contact forces, play a central role for slow granular flows. These agitations are generated in flowing regions, but travel deep inside the quiescent zones, and lead to a nonlocal rheology.     

Measurement of grain–wall contact forces in a granular bed using frequency-scanning interferometry

Micro-mechanical theories have recently been developed to model the propagation of force through a granular material based on single grain interactions. We describe here an experimental technique, developed to validate such theories, that is able to measure the individual contact forces between the grains and the wall of the containing vessel, thereby avoiding the spatial averaging effect of conventional pressure transducers. The method involves measuring interferometrically the deflection of an interface within a triple-layer elastic substrate consisting of epoxy, silicone rubber, and glass. A thin coating of gold between the epoxy and rubber acts as a reflective film, with the reference wave provided by the glass/air interface. Phase shifting is carried out by means of a tunable laser. Phase difference maps are calculated using a 15-frame phase-shifting formula based on a Hanning window. The resulting displacement resolution of order 1 nm allows the wall stiffness to be increased by some two orders of magnitude compared to previously described methods in the literature.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

Surface modes in metal–insulator composites with strong interaction of metal particles

We theoretically examine plasmonic resonance excited between two close metallic grains embedded into a dielectric matrix. The grains sizes are assumed to be much less than the wavelength of the electromagnetic wave in the dielectric medium and the grain’s separation is assumed to be much smaller than the grains sizes. A qualitative scheme is developed that enables one to estimate frequency of the plasmonic resonance and value of the field enhancement inside the gap. Our general arguments are confirmed by rigorous analytic solution of the problem for simplest geometry—two identical spherical grains.     

Elastic wave propagation and scattering in solids with uniaxially aligned cracks

In this article, elastic wave propagation and scattering in a solid medium permeated by uniaxially aligned penny-shaped microcracks are studied. The crack alignment refers to the case in which the unit normals of all cracks are randomly oriented within a plane of isotropy. The analysis is restricted to the limit of the noninteraction approximation among individual cracks. Explicit expressions for attenuations and wave speeds of the shear horizontal, quasilongitudinal, and quasishear vertical waves are obtained using stochastic wave theory in a generalized dyadic approach. The ensemble average elastic wave response is governed by the Dyson equation, which is solved in terms of the anisotropic elastic Green's dyadic. The analysis of expressions is limited to frequencies below the geometric optics limit. The resulting attenuations are investigated in terms of the directional, frequency, and damage dependence. In particular, the attenuations are simplified considerably within the low frequency Rayleigh regime. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters.