Anisotropic nonlinear elasticity in a spherical bead pack: influence of the fabric anisotropy

Stress-strain measurements and ultrasound propagation experiments in glass bead packs have been simultaneously conducted to characterize the stress-induced anisotropy under uniaxial loading. These measurements, realized respectively with finite and incremental deformations of the granular assembly, are analyzed within the framework of the effective medium theory based on the Hertz-Mindlin contact theory. Our work shows that both compressional and shear wave velocities and consequently the incremental elastic moduli agree fairly well with the effective medium model by Johnson et al. [J. Appl. Mech. 65, 380 (1998)], but the anisotropic stress ratio resulting from finite deformation does not at all. As indicated by numerical simulations, the discrepancy may arise from the fact that the model doesn't properly allow the grains to relax from the affine motion approximation. Here we find that the interaction nature at the grain contact could also play a crucial role for the relevant prediction by the model; indeed, such discrepancy can be significantly reduced if the frictional resistance between grains is removed. Another main experimental finding is the influence of the inherent anisotropy of granular packs, realized by different protocols of the sample preparation. Our results reveal that compressional waves are more sensitive to the stress-induced anisotropy, whereas the shear waves are more sensitive to the fabric anisotropy, not being accounted in analytical effective medium models.Comment: 9 pages, 8 figure

A review of the state of art in applying Biot theory to acoustic propagation through the bone

Understanding the propagation of acoustic waves through a liquid-perfused porous solid framework such as cancellous bone is an important pre-requisite to improve the diagnosis of osteoporosis by ultrasound. In order to elucidate the propagation dependence upon the material and structural properties of cancellous bone, several theoretical models have been considered to date, with Biot-based models demonstrating the greatest potential. This paper describes the fundamental basis of these models and reviews their performance

Nonlinearity parameters of polymers

Three types of acoustic nonlinearity parameters for solids are discussed. The results of measurements of these parameters for three polymers--polymethyl methacrylate, Polystyrene, and polysulfone--are presented.;The author has developed a new technique, using piezoelectric transducers directly bonded to the specimens, which allows the measurements of fundamental and second harmonics generated in the solids, and thereby the determination of nonlinearity parameter {dollar}\beta\sb3{dollar}, which is the ratio of a linear combination of second- and third-order elastic coefficients to the second-order elastic coefficient.;The second nonlinearity parameter, B/A can be determined from the temperature and pressure derivatives of the sound velocity. We derive its exact relationship for the case of solids. The results from the two techniques are shown to be consistent.;The pressure derivative of the sound velocity is also related to the Gruneisen parameter, which can be used to describe the anharmonicity of interactions in polymer molecules, especially of interchain vibrations. The interchain specific heat for these polymers is then calculated from the Gruneisen parameters; and the characterization of polymers by using these thermoacoustic parameters is discussed

Nonlinear ultrasonic test using PZT transducer for crack detection in metallic component

A crack detection technique based on nonlinear ultrasonic is developed in this study. Acoustic waves at a chosen frequency are generated using an actuating lead zirconate titanate (PZT) transducer, and they travel through the target structure before being received by a sensing PZT wafer. Unlike an undamaged medium, a cracked medium exhibits high acoustic nonlinearity, which is manifested as harmonics in the power spectrum of the received signal. Experimental results also indicate that the harmonic components increase nonlinearly in magnitude with increasing amplitude of the input signal. The proposed technique identifies the presence of cracks by looking at the two aforementioned features: harmonics and their nonlinear relationship to the input amplitude. The effectiveness of the technique has been tested on aluminum specimens