Complete elastic characterization of viscoelastic materials by dynamic measurements of the complex bulk and Young's moduli as a function of temperature and hydrostatic pressure

Two independent systems to measure the dynamic complex Young's and bulk moduli of viscoelastic materials as a function of temperature and hydrostatic pressure are described. In the Young's modulus system, a bar-shaped sample is adhered to a piezoelectric shaker and mounted vertically inside an air-filled pressure vessel. Data are obtained using both the traditional resonant approach and a wave-speed technique. In the bulk modulus system, the compressibility of a sample of arbitrary shape immersed in Castor oil and placed inside a pressure chamber is measured. Data can be obtained at frequencies typically ranging from 50 Hz to 5 kHz, at temperatures comprised between −2 and 50 °C and under hydrostatic pressures ranging from 0 to 2 MPa (Young's), or 6.5 MPa (bulk). Typical data obtained with both systems are presented, and it is shown how these data can be combined to completely characterize the elasticity of the material under investigation. In particular, they can be used to obtain experimental values of the complex Poisson's ratio, whose accurate measurement is otherwise quite challenging to perform directly. As an example, the magnitude and loss tangent of Poisson's ratio are presented for a nearly incompressible rubber.     

黏弹细棒中直达波提取及其动态力学参数的宽频测试

黏弹性材料的动态力学参数可通过对材料样品中纵波测试并结合波速法计算得到。由于测试样品尺寸的限制,除了高损耗材料在高频范围外,不管是在样品端头或侧面都难以获得准确的直达波信号,导致参数测量不准确。针对这个问题,对一端固定一端自由的黏弹性细棒中的纵波传播过程进行了分析,提出了黏弹性细棒直达波提取的方法,并实现了黏弹性材料动态力学参数的宽频测试。采用宽带脉冲作为测试激励信号,利用两台激光测振仪对细棒的固定端和自由端的振动速度进行测试,计算得到细棒自由端处的直达波。然后,利用提取出的直达波信号进行波速法计算,得到了黏弹性细棒宽频范围内的储能模量和损耗因子,宽频脉冲测试结果与黏弹仪测试结果相吻合,验证了该方法的有效性。基于直达波提取的宽频测试方法不仅效率高,而且可以使波速法应用于更低的频段。     

固体杨氏模量的测量

通过测量超声波在固体介质中传播的纵波传播速度,进一步测量该固体的杨氏模量,得到了测量固体杨氏模量的一种新方法。     

NONLINEAR WAVES PROPAGATING IN AN INHOMOGENEOUS BLOOD VESSEL

A model for describing blood pressure propagation wave in artery is proposed. Considering blood viscosity, slowly varying arterial parameters and arterial bifurcations, we obtain the dynamical equation of blood flow. We show that the blood viscosity attenuate the nonlinear blood wave amplitude mainly in small artery. On the other hand, the variation of arterial parameters (such as radius and Young's modulus) amplify the amplitude of the nonlinear blood wave in large arteries. We also investigate how the nonlinear blood wave (or a soliton) is reflected and transmitted at the arterial bifurcations. It can be concluded that the parameters at the bifurcation determine whether there is substantial reflection or not, but the transmission in each bifurcation is approximately the same as the incident wave.     

驻波法测杨氏模量及误差分析

驻波法运用驻波原理,采用人为控制金属丝形变,测出金属丝驻波基频,得出其张力,从而求出金属丝杨氏模量.相对传统方法,驻波法避免了金属丝直径和形变的测量,其不确定度基本上仅由千分尺精度决定,故而具有操作简单,测量准确度高的特点.     

Radiofrequency electrode vibration-induced shear wave imaging for tissue modulus estimation: a simulation study

Quasi-static electrode displacement elastography, used for in-vivo imaging of radiofrequency ablation-induced lesions in abdominal organs such as the liver and kidney, is extended in this paper to dynamic vibrational perturbations of the ablation electrode. Propagation of the resulting shear waves into adjoining regions of tissue can be tracked and the shear wave velocity used to quantify the shear (and thereby Young's) modulus of tissue. The algorithm used utilizes the time-to-peak displacement data (obtained from finite element analyses) to calculate the speed of shear wave propagation in the material. The simulation results presented illustrate the feasibility of estimating the Young's modulus of tissue and is promising for characterizing the stiffness of radiofrequency-ablated thermal lesions and surrounding normal tissue.     

Numerical study of pressure relationships between sample and calibrant inside the diamond anvil cell

We present isotropic, elastic-plastic finite element calculations detailing the pressure relationship between an inclusion and its surrounding matrix, subject to an externally imposed hydrostatic strain. In general, the inclusion and the matrix have different values of hydrostatic pressure, depending on their absolute and relative values of Young's modulus and Poisson's ratio. A series of finite element models was used to explore the parameter space of the elastic and plastic properties of an inclusion within a matrix. In all cases where there is insufficient relaxation of the nonhydrostatic stress, the material with the higher bulk modulus will also have a higher pressure, regardless of the shear moduli. The complete data set was subjected to a Pareto analysis to determine the main and secondary effects which influence the final result, expressed as the ratio of the pressure of the matrix to that of the inclusion. The four most important factors which determine the pressure ratio of an inclusion and matrix are the Young's modulus of the matrix, the interaction of the Young's modulus and the yield strength of the matrix material, the Young's modulus of the inclusion, and the interaction of the Young's modulus of the inclusion with the yield strength of the matrix material. The yield strength of the inclusion has a statistically insignificant effect on the results. This information provides guidelines for designing the most effective combinations of unknowns and material standards to minimize pressure errors in equation of state measurements.     

LY-12铝高温凝聚态动力学性质研究——高温弹性模量的测定

 金属材料的高温动态力学性能是材料科学领域中的重要方面。本文介绍LY-12合金铝在常温至450 ℃的温度区间内和动载下（应变率为10³/s），材料弹性模量的研究。此项研究采用的试验装置为一维Hopkinson压杆及管式高温炉。应用一维弹性应力波传播理论，测得LY-12铝试件在不同温度T条件下的声速c(T)，按照c(T)=[E(T)/ρ(T)]^1/2，获得杨氏模量E(T)随温度的变化曲线。     

Determination of the complex Young and shear dynamic moduli of viscoelastic materials

The Young and shear dynamic moduli of viscoelastic materials are determined from laser vibrometric measurements of the surface motion of a three-dimensional sample excited by a piezoelectric actuator inside a chamber with controllable temperature and static pressure. The moduli are estimated from an inversion code that minimizes the difference between the data and the predictions from a finite element model in which the elastic moduli are the adjustable parameters. The technique is first used to measure the dynamic properties of homogeneous samples and the results are compared with those obtained by the standard rod resonance technique. Results are then obtained with microvoided samples in the 0.5-3 kHz frequency range, at temperatures ranging from 7 to 40 degrees C, and static pressures ranging from ambient to 34 atm (3.45 MPa or 500 psi). The limitations of the technique are discussed.     

Estimation of dynamic elastic constants from the amplitude and velocity of Rayleigh waves

In this paper a method is proposed to characterize the elasticity of isotropic linear materials from the generation and detection of an acoustic surface wave. For the calculation of the elastic constants, it is sufficient that only one of the faces of the sample be accessible. The methodology is based on both the measurement of the Rayleigh wave velocity and on the determination of the normal to longitudinal amplitude ratio calculated from the normal and longitudinal components of the displacement of a point. The detection of two consecutive surface wave pulses using a single experimental setup permits the determination of the elastic constants. The method is applied to calculate Young's modulus and Poisson's ratio of an aluminum sample as well as their systematic uncertainties. The results obtained give a relative uncertainty for Young's modulus on the order of the sixth part of that calculated for Poisson's ratio.     

Optically monitored high-pressure gas loading apparatus for diamond anvil cells

We describe a high-pressure system built to load rare gases (He, Ar, Ne) in various types of diamond anvil cells, at room temperature. These gases are used as pressure transmitting media to obtain the best hydrostatic compression conditions in high-pressure experiments. Optical windows allow control of the loading process. The loading success rate is close to 100% and the initial pressures in the diamond anvil cell are in between 0.2 and 1?GPa. This system can easily be adapted for loading of various gaseous samples, including gas mixtures, which generally cannot be loaded by cryogenic methods.     

Finite element simulation of wave propagation in an axisymmetric bar

An accurate solution for high-frequency pulse propagation in an axisymmetric elastic bar is obtained using a new finite element technique that yields accurate non-oscillatory solutions for wave propagation problems in solids. The solution of the problem is very important for the understanding of dynamics experiments in the split Hopkinson pressure bar (SHPB). In contrast to known approaches, no additional assumptions are necessary for the accurate solution of the considered problem. The new solution helps to elucidate the complicated distribution of parameters during high-frequency pulse propagation down the bar as well as to estimate the applicability of the traditional dispersion correction used in the literature for the analysis of wave propagation in a finite bar. Due to the dimensionless formulation of the problem, the numerical results obtained depend on Poisson's ratio, the length of the bar and the pulse frequency, and are independent of Young's modulus, the density and the radius of the bar.     

Material property estimation for tubes and arteries using ultrasound radiation force and analysis of propagating modes

Arterial elasticity has been proposed as an independent predictor of cardiovascular diseases and mortality. Identification of the different propagating modes in thin shells can be used to characterize the elastic properties. Ultrasound radiation force was used to generate local mechanical waves in the wall of a urethane tube or an excised pig carotid artery. The waves were tracked using pulse-echo ultrasound. A modal analysis using two-dimensional discrete fast Fourier transform was performed on the time-space signal. This allowed the visualization of different modes of propagation and characterization of dispersion curves for both structures. The urethane tube/artery was mounted in a metallic frame, embedded in tissue-mimicking gelatin, cannulated, and pressurized over a range of 10-100 mmHg. The k-space and the dispersion curves of the urethane tube showed one mode of propagation, with no effect of transmural pressure. Fitting of a Lamb wave model estimated Young's modulus in the urethane tube around 560 kPa. Young's modulus of the artery ranged from 72 to 134 kPa at 10 and 100 mmHg, respectively. The changes observed in the artery dispersion curves suggest that this methodology of exciting mechanical waves and characterizing the modes of propagation has potential for studying arterial elasticity.     

IrB和IrB$lt;sub$gt;2$lt;/sub$gt;力学性质的第一性原理计算

采用平面波赝势密度泛函理论对0–100 GPa静水压下P₁ -IrB（空间群Pnma）和P₅ -IrB₂（空间群Pmmn）结构的平衡态晶格常数、弹性常数等性质进行了研究. 研究结果表明,P₁ -IrB不可压缩性随着压强的增加而增强;P₅ -IrB₂ 结构在0–100 GPa范围内弹性常数、体弹模量、剪切模量均呈现出有规律的变化,当所加压强为50 GPa时,杨氏模量和在b方向的晶格常数发生异常变化. 对零压下P₁ -IrB和P₅ -IrB₂ 的电子结构的研究发现,二者均没有一个明显的带隙,主要原因为Ir原子和B原子间的共价作用. 从P₁ -IrB和P₅ -IrB₂的能带结构和态密度图可以发现这两种结构均有金属性. 关键词： 1 -IrB')" href="#">P₁ -IrB 5-IrB₂')" href="#">P₅-IrB₂ 第一性原理 力学性质     

Influence of static compression on mechanical parameters of acoustic foams

The modification of elastic properties of compressed acoustic foams is investigated. The porous sample is first submitted to a static compression and then to a dynamic excitation of smaller amplitude, corresponding to acoustical applications. The static compression induces the modification of the dynamic elastic parameters of the material. This work focuses on Young's modulus. The variation is measured with two different experimental methods: The classical rigidimeter and an absorption measurement. The effective Young's modulus is directly measured with the first method and is indirectly determined through the quarter-wave length resonance of the frame with the second one. The results of the two measurements are compared and give similar tendencies. The variation of the dynamic Young's modulus as a function of the degree of compression of the sample is shown to be separated in several zones. In the zones associated with weak compression (those usually zones encountered in practice), the variation of the effective Young's modulus can be approximated by a simple affine function. The results are compared for different foams. A simple model of the dependency of the Young's modulus with respect to the static degree of compression is finally proposed for weak compressions.     

Transverse elasticity of multi-walled carbon nanotubes

A discrete shell model is proposed to describe the radial deformation of carbon nanotubes under a hydrostatic pressure and the radial Young's modulus of (single- or multi-walled) nanotubes is obtained. It is found that the radial modulus decreases with increasing tube diameter while increases with increasing number of layers. The computational results agree well with the previous results of SWNTs and indicate that the radial modulus of carbon nanotubes is independent of the Poisson's ratio.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

Experimental observation of the slowdown of optical beams by a volume-index grating in a photorefractive LiNbO3 crystal

We investigate the group velocity of light in a one-dimensional volume-index grating inside a photorefractive LiNbO>(3) crystal. The slowdown of the group electromagnetic propagation is observed experimentally by tuning of the wave number of the optical beam close to the outside edge of the forbidden bandgap. We obtain a large group index of up to 7.5 in a 3.5-cm crystal sample. The group index is compared with the result of a theoretical derivation. The results are presented and discussed.     

空位结构缺陷对C纳米管弹性性质的影响

用分子动力学方法对不同空位缺陷的扶手椅型与锯齿型单壁C纳米管杨氏弹性模量进行了计算和分析. 结果表明：扶手椅型（5, 5）, （10,10）和锯齿型（9, 0）, （18, 0） 纳米管在无缺陷时其杨氏模量分别为948,901和804,860 GPa. 随管径的增大,扶手椅型和锯齿型单壁C纳米管弹性模量分别减小和增大,表现出完全不同的变化规律. 随着C纳米管中单点空位缺陷的均匀增加,杨氏模量下降,当缺陷比率增加到一定程度时,杨氏模量下降骤然趋缓,形成一下降平台;双空位缺陷对C纳米管杨氏模量的影响与其分布方向有关;随单点空位缺陷间原子数的增加,在轴向上,杨氏模量下降到某一值小幅波动,而在周向上杨氏模量先下降,然后上升到某一稳定值. 随两单点空位缺陷的空间距离进一步增大,杨氏模量又呈微降趋势. 通过分子间σ键与π键特征及缺陷间近程电子云耦合作用规律与空位缺陷内部5-1DB缺陷的形成特点等理论对上述规律进行了分析. 关键词： 空位缺陷 C纳米管 分子动力学 杨氏模量     

Weak nonlinear propagation of sound in a finite exponential horn.

This article presents an approximate solution for weak nonlinear standing waves in the interior of an exponential acoustic horn. An analytical approach is chosen assuming one-dimensional plane-wave propagation in a lossless fluid within an exponential horn. The model developed for the propagation of finite-amplitude waves includes linear reflections at the throat and at the mouth of the horn, and neglects boundary layer effects. Starting from the one-dimensional continuity and momentum equations and an isentropic pressure-density relation in Eulerian coordinates, a perturbation analysis is used to obtain a hierarchy of wave equations with nonlinear source terms. Green's theorem is used to obtain a formal solution of the inhomogeneous equation which takes into account linear reflections at the ends of the horn, and the solution is applied to the nonlinear horn problem to yield the acoustic pressure for each order, first in the frequency and then in the time domain. In order to validate the model, an experimental setup for measuring fundamental and second harmonic pressures inside the horn has been developed. For an imposed throat fundamental level, good agreement is obtained between predicted and measured levels (fundamental and second harmonic) at the mouth of the horn.