Comparative investigation of elastic properties in a trabecula using micro-Brillouin scattering and scanning acoustic microscopy

Micro-Brillouin scattering (μ-BR) and a 200 MHz scanning acoustic microscope (SAM) with similar spatial resolutions were applied to evaluate tissue elastic properties in two directions in a trabecula. Acoustic impedance measured by SAM was in the range of 5-9 Mrayl. Wave velocities determined by μ-BR were in the range of (4.75-5.11) × 10(3) m/s. Both exhibited a similar trend of variation across the trabecula and were significantly correlated (R(2) = 0.63-0.67, p < 0.01). μ-BR is useful for the evaluation of tissue stiffness within a trabecula. Combined with SAM or nanoindentation, it can provide additional information to assess elastic anisotropy at the micro-scale.     

Elastic constants measurement of anisotropic Olivier wood plates using air-coupled transducers generated Lamb wave and ultrasonic bulk wave

A hybrid elastic wave method is applied to determine the anisotropic constants of Olive wood specimen considered as an orthotropic solid. The method is based on the measurements of the Lamb wave velocities as well as the bulk ultrasonic wave velocities. Electrostatic, air-coupled, ultrasonic transducers are used to generate and receive Lamb waves which are sensitive to material properties. The variation of phase velocity with frequency is measured for several modes propagating parallel and normal to the fiber direction along a thin Olivier wood plates. A numerical model based mainly on an optimization method is developed; it permits to recover seven out of nine elastic constants with an uncertainty of about 15%. The remaining two elastic constants are then obtained from bulk wave measurements. The experimental Lamb phase velocities are in good agreement with the calculated dispersion curves. The evaluation of Olive wood elastic properties has been performed in the low frequency range where the Lamb length wave is large in comparison with the heterogeneity extent. Within the interval errors, the obtained elastic tensor doesn’t reveal a large deviation from a uniaxial symmetry.     

Ultrasonic characterization of Cu-Al-Ni single crystals lattice stability in the vicinity of the phase transition

Measurements of elastic constants of the austenite phase when approaching the phase transformation either upon cooling or stressing is of the crucial interest for the shape memory alloy field. Acoustic properties (wave velocity and also attenuation changes) of the Cu-Al-Ni single crystal were investigated in situ during stress-induced martensitic transformation at constant (room) temperature. The parent austenite cubic lattice of the Cu-Al-Ni exhibits very high elastic anisotropy (anisotropy factor A approximately 12). The measurements were made using nine combinations of (i) applied uniaxial compression in a given crystal direction, (ii) the wave propagation and (iii) polarization vectors. The chosen configurations are sufficient for evaluation of all independent third order elastic constants (TOEC). The longitudinal modes were also measured by the immersion technique, using the transducer pair in a water tank installed on the testing machine. The device works as "a ultrasonic extensometer" measuring a transverse strain of the specimen. The dependencies of both natural and initial wave velocities on the applied stress may be evaluated. Three elastic constants of the stress-induced martensite were determined. The elastic properties were found to vary with the increasing stress above the Ms transformation temperature, which is interpreted as a precursor for the martensitic transformation. The onset of the transformation was additionally identified from the acoustic emission measurement.     

Effect of porosity on effective diagonal stiffness coefficients (cii) and elastic anisotropy of cortical bone at 1 MHz: a finite-difference time domain study

Finite-difference time domain (FDTD) numerical simulations coupled to real experimental data were used to investigate the propagation of 1 MHz pure bulk wave propagation through models of cortical bone microstructures. Bone microstructures were reconstructed from three-dimensional high resolution synchrotron radiation microcomputed tomography (SR-muCT) data sets. Because the bone matrix elastic properties were incompletely documented, several assumptions were made. Four built-in bone matrix models characterized by four different anisotropy ratios but the same Poisson's ratios were tested. Combining them with the reconstructed microstructures in the FDTD computations, effective stiffness coefficients were derived from simulated bulk-wave velocity measurements. For all the models, all the effective compression and shear bulk wave velocities were found to decrease when porosity increases. However, the trend was weaker in the axial direction compared to the transverse directions, contributing to the increase of the effective anisotropy. On the other hand, it was shown that the initial Poisson's ratio value may substantially affect the variations of the effective stiffness coefficients. The present study can be used to elaborate sophisticated macroscopic computational bone models incorporating realistic CT-based macroscopic bone structures and effective elastic properties derived from muCT-based FDTD simulations including the cortical porosity effect.     

Brillouin scattering study of epoxy adhesive layers during cure

The isothermal curing process of thin epoxy adhesive layers (mixture of a bisphenol A-based epoxy prepolymer and an aliphatic diamine curing agent) has been investigated. The Brillouin scattering technique with 90 degrees A scattering geometry enables simultaneous measurements of longitudinal and shear wave properties in the GHz range. Observed longitudinal and shear wave velocities showed similar changes during cure. They rapidly increased and gradually became constant, reflecting the elastic changes of the epoxy layer. The final velocities, however, clearly depended on the curing temperature. Taking the glass transition process of epoxy resins into consideration, these curing behaviors in thin layers are discussed.     

Application of narrow band laser ultrasonics to the nondestructive evaluation of thin bonding layers

In this paper, a modified laser induced grating technique (LIG) has been utilized to generate narrow band surface waves in an epoxy-bonded copper-aluminum layered structure. A high performance optical interferometer system was utilized to detect the laser-generated surface waves. The dispersion of surface wave in an epoxy-bonded copper-aluminum specimen was measured and compared with the theoretical solution. An inverse algorithm based on the simplex method was then introduced to determine the bonding thickness as well as the elastic properties of the bonding layer. The inversion results demonstrated that the thickness in the microm range or the elastic properties of the bonding layer could be successfully determined.     

A first-principles study on the structural and elastic properties and the equation of state of wurtzite-type cadmium selenide under pressure

A first-principles investigation on the crystal structural and elastic properties and the equation of state of wurtzite-type cadmium selenide (w-CdSe) has been conducted using the plane-wave pseudo-potential density functional theory and the quasi-harmonic Debye model. The elastic constants, the aggregate elastic moduli, the elastic anisotropy, and Poisson's ratio under pressure have been investigated. Our calculated equilibrium lattice constants, the elastic constants, and the aggregate elastic moduli at zero pressure are in good agreement with the experimental data and other theoretical results. The variations in the compressional and shear elastic wave velocities with pressure at zero temperature up to pressure 2.7 GPa have been studied; the computed Debye temperature at zero pressure and zero temperature is in reasonable agreement with the result of Bonello et al., In addition, the equation of state of w-CdSe in the pressure range of 0–2.7 GPa and up to a temperature of 900 K has also been obtained.     

EuS高压相变及其弹性和热力学性质

采用平面波赝势密度泛函理论,利用第一性原理的方法研究了EuS的晶体结构、高压相变以及弹性性质．计算结果和实验值以及前人利用不同计算模型得到的理论值相吻合．研究了EuS的弹性常数、弹性模量和弹性的各向异性等力学性质随压力变化的趋势．同时研究了泊松比、德拜温度及纵波和横波的弹性波速随压力的变化趋势．基于德拜模型,进而研究了EuS在0～800 K和0～60 GPa下相变前后的热膨胀系数、热熔、Grüneisen参数等热力学性质．     

First-Principles Calculations for Elastic Properties of ZnS under Pressure

The pressure dependence of elastic properties of ZnS in zinc-blende （ZB） and wurtzite （WZ） structures are investigated by the generalized gradient approximation （GGA） within the plane-wave pseudopotential density functional theory （DFT）. Our results are in good agreement with the available experimental data and other theoretical results. From the high-pressure elastic constants obtained, we find that the ZB and WZ structures of ZnS are unstable when the applied pressures are larger than 15.8 GPa and 21.3 GPa, respectively. The sound velocities along different directions for the two structures are also obtained. It is shown that as pressure increases, the sound velocities of the shear wave decrease, and those of all the longitudinal waves increase. An analysis has been made to reveal the anisotropy and highly noneentral forces in ZnS.     

Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones

Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.     

Molecular Dynamics Simulations of the Elastic Anisotropy of Pd at Extreme Conditions

It is very interesting to discover the elastic properties of engineering material palladium, especially its elastic anisotropy along Hugoniot states. We here investigate the evolution of its high pressure and temperature(PT) elastic ansotropy along Hugoniot using molecular dynamics simulations based on accurate classical interatomic potential. In order to testify the validity of the interatomic potential of Pd in describing the high PT elastic properties, we calculate its isothermal and adiabatic elastic moduli using molecular dynamics method. The obtained data are in good agreement with experimental data. From the isothermal elastic constants, we deduce the Hugoniot acoustic velocities and find that the resulting data are in good agreement with experimental acoustic velocity data. Based on the reliable elastic constants, we further investigate the spacial elastic ansotropy along Hugoniot PT states. It is found that the spacial elastic anisotropy of Pd increases along Hugoniot states.     

Application of Biot's theory to ultrasonic characterization of human cancellous bones: determination of structural, material, and mechanical properties

This paper is devoted to the experimental determination of distinctive macroscopic structural (porosity, tortuosity, and permeability) and mechanical (Biot-Willis elastic constants) properties of human trabecular bones. Then, the obtained data may serve as input parameters for modeling wave propagation in cancellous bones using Biot's theory. The goal of the study was to obtain experimentally those characteristics for statistically representative group of human bones (35 specimens) obtained from a single skeletal site (proximal femur). The structural parameters were determined using techniques devoted to the characterization of porous materials: electrical spectroscopy, water permeametry, and microcomputer tomography. The macroscopic mechanical properties, Biot-Willis elastic constants, were derived based on the theoretical consideration of Biot's theory, micromechanical statistical models, and experimental results of ultrasonic studies for unsaturated cancellous bones. Our results concerning structural parameters are consistent with the data presented by the other authors, while macroscopic mechanical properties measured within our studies are situated between the other published data. The discrepancies are mainly attributed to different mechanical properties of the skeleton frame, due to strong structural anisotropy varying from site to site. The results enlighten the difficulty to use Biot's theory for modeling wave propagation in cancellous bone, implying necessity of individual evaluation of input parameters.     

First-principles predictions of anisotropies in elasticity and sound velocities of CsCl-type refractory intermetallics: TiTM,ZrTM and HfTM (TM = Fe,Ru, Os)

ABSTRACT

Structural properties, elastic properties, sound velocities and Debye temperatures of CsCl-type refractory TiTM, ZrTM and HfTM (TM?=?Fe, Ru, Os) intermetallics were investigated using first-principles calculations. The calculated equilibrium lattice parameters are coincided with the reported experimental and theoretical data. Based on single-crystal elastic constants, polycrystalline elastic moduli, Poisson’s ratios, sound velocities and Debye temperatures were evaluated. Anisotropies in elastic moduli of these CsCl-type intermetallics were discussed by elastic anisotropy indexes, three-dimensional surface constructions and their projections, and directional elastic modulus. The results showed that ZrFe has the highest elastic anisotropy and ZrOs presents the lowest one. Finally, sound velocities, Debye temperatures and their anisotropies were also calculated and discussed.     

First-principles calculations on elasticity of under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c_ij, the aggregate elastic moduli (B,G,E), Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.     

Second-order and third-order elastic constants of B95 aluminum alloy and B95/nanodiamond composite

All independent second-order and third-order elastic constants in B95 aluminum alloy and B95/nanodiamond composite have been determined. To determine the second-order elastic constants, the densities and velocities of longitudinal and shear bulk acoustic waves in the materials under study have been measured. To quantitatively characterize the nonlinear elastic properties, the third-order elastic constants (TOECs) of B95 alloy and B95/nanodiamond composite have been determined. The Thurston-Brugger method has been used to experimentally determine the TOECs. For this purpose, the relative changes in the bulk wave velocity have been experimentally measured depending on the uniaxial compression applied to the samples under study and all independent TOECs have been calculated. The elastic wave velocities have been measured by the ultrasonic pulse method at a frequency of 10 MHz. The results obtained have been discussed.     

High-pressure elastic properties of solid argon to 70 GPa

The acoustic velocities, adiabatic elastic constants, bulk modulus, elastic anisotropy, Cauchy violation, and density in an ideal solid argon (Ar) have been determined at high pressures up to 70 GPa in a diamond anvil cell by making new approaches of Brillouin spectroscopy. These results place the first complete study for elastic properties of dense Ar and provide an improved basis for making the theoretical calculations of rare-gas solids over a wide range of compression.     

Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory

Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.     

Elastic measurements of layered nanocomposite materials by Brillouin spectroscopy

Surface Brillouin spectroscopy makes it possible to measure surface elastic wave propagation parameters at frequencies up to 20 GHz or more. This enables us to measure the elastic properties of surface layers only a small fraction of a micrometre thick. The wavelength and incident angle of the light determine the wavenumber of surface elastic waves (SAW) that scatter the light inelastically, and their frequency can be found by measuring the change in wavelength of the scattered light. By analysing the elastic wave modes present in the surface, the elastic properties can be deduced. We have used this technique to measure the elastic properties of layered nanocomposite materials, which are widely used in the packaging industry. 12 microns polymer films (PET) were coated with glass oxide layers of thickness as little as 25 nm, to give transparent nanocomposite structures with excellent gas barrier properties. In order to understand and model the behaviour of these films under deformation, it is necessary to determine the elastic properties of the different layers. Evaluation of the elastic properties presents several challenges. First, the oxide layers are much thinner than the wavelengths of the surface phonons in surface Brillouin spectroscopy (and hence the depth probed), which usually lie in the range 250-500 nm. The anisotropic elastic properties of the PET substrate must therefore be measured accurately, and this can be done using bulk Brillouin spectroscopy. Second, a thin layer of metal (usually 10-20 nm) must be deposited on the glass surface so that the surface phonons scatter the light effectively. The elastic properties of the glass layer can then be deduced from surface Brillouin spectroscopy measurements, by simulating the surface wave modes of the metal/glass/polymer composite, and adjusting the parameters to give the best fit. In this way it is possible to observe how the properties of the glass vary as a function of thickness, and in turn to understand how to improve systematically the properties under deformation.     

Fabric dependence of quasi-waves in anisotropic porous media

Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor--a quantitative stereological measure of the degree of structural anisotropy of bone--into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.     

Observation of ultrasound velocity gradient in fullerene ceramics by acoustic microscopy

A scanning acoustic microscope is used to study the distribution of elastic properties in small samples (O 3 x 2 mm3) of new hard phases of C60. The specimens under investigation were synthesized from pure C60 powder under pressure P = 8 GPa in the temperature range 500-1650 K. The time-of-flight mode was used for bulk sound wave velocity determination in a direction parallel to the cylinder's axis. Longitudinal sound wave velocities greater than 10,000 m/s were found for all specimens treated at temperatures higher than 1000 K. Using the B-scan mode allowed us to observe the velocity gradient in the sample's periphery. The heterogeneous internal structure of the specimen is visualized in the images formed in C- and B-scan modes.