Nonlinear Inversion of Ultrasonic Guided Waves for in Vivo Evaluation of Cortical Bone Properties

Ultrasonic guided waves (UGW), which propagate throughout the whole thickness of cortical bone, are attractive in the early diagnosis of osteoporosis. However, it is challenging due to the impact of soft tissue and the inherent difficulties related to the multiparametric inversion of cortical bone quality factors, such as cortical thickness and bulk wave velocities. Therefore, an UGW based multiple-parameter inversion algorithm is developed to predict strength-related factors in this research. In simulation, a free plate (cortical bone) and a bilayer plate (soft tissue and cortical bone) are used to validate the proposed method. The inverted cortical thickness (CTh), longitudinal velocity (V L ) and transverse velocity (V T ) are in accordance with the true value. Then four bovine cortical bone plates are used in the in vitro experiments. Compared with the reference values, the relative errors for cortical thicknesses are 3.96%, 0.83%, 2.87% and 4.25% respectively. In the in vivo measurements, ultrasonic guided waves are collected from ten volunteers’ tibia. The theoretical dispersion curves depicted by the estimated parameters (V T , V L , CTh) match well with the extracted experimental ones. In comparison to the dual-energy x-ray absorptiometry (DXA), the results show that the estimated transverse velocity and cortical thickness are highly sensitive to the osteoporosis. Therefore, these two parameters (CTh and V T ) of long bones have potential to diagnose bone status in clinical applications.

Evaluation and Validation of HF Radar Swell and Wind wave Inversion Method

An examination of the applicability and accuracy of the empirical wave inversion method in the presence of swell waves is presented. The ability of the method to invert Doppler spectra to wave directional spectra and bulk wave parameters is investigated using one-month data from a 12 MHz WERA High Frequency (HF) radar system and in-situ data from a wave buoy. Three different swell inversion models are evaluated: LPM (Lipa et al. 1981), WFG (Wang et al. 2016) and EMP, an empirical approach introduced in this study. The swell inversions were carried out using two different scenarios: (1) a single beam from a single radar site and two beams from a single radar site, and (2) two beams from two sites (a single beam per site) intersecting each other at the buoy location. The LPM method utilized using two beams from two different sites was found to provide the best estimations of swell parameters (swell height RMS error 0.24m) and showed a good correlation with the partitioned swell in-situ values. For the wind wave inversion, the empirical method presented here is used with an empirical coefficient of 0.3 which seems to be suitable for universal application for all radar operating frequencies. The inverted swell parameters are used to create a swell spectrum which is combined with the inverted wind wave spectrum to create a full directional wave spectrum. The wave inversion method presented in this study although empirical does not require calibration with in situ data and can be applied to any beam forming system and operating frequency.

A Feasibility Study for a Nonlinear Guided Wave Mixing Technique

Ultrasonic non-destructive testing is an effective means of examining objects without destroying them. Among such testing, ultrasonic nonlinear evaluation is used to detect micro-damage, such as corrosion or plastic deformation. In terms of micro-damage evaluation, the data that comes from amplitude comparison in the frequency domain plays a significant role. Its technique and parameter are called ultrasonic nonlinear technique and nonlinearity. A certain portion of nonlinearity comes from the equipment system, while the other portion of nonlinearity comes from the material. The former is system nonlinearity, while the latter is material nonlinearity. System nonlinearity interferes with interpretation, because its source is not from the material. In this study, in order to minimize system effects, a mixing technique is implemented. To use the large area inspection ability of the guided wave, the main research issue in this paper is focused on the guided wave mixing technique. Moreover, several bulk wave mixing theory equations become good concepts for guided wave mixing theoretical study, and the conventional nonlinear technique and guided wave mixing experimental results are compared in this study to confirm the reliability. This technique can play an important role in quantitatively discriminating fine damage by minimizing the nonlinearity of the equipment system.

Mathematical simulation of elastoplastic deformation in cubic materials with an account of anisotropic bulk compressibility

It was shown for the first time that when modelling the deformation of materials with cubic symmetry (at full stress), the rotation of the computational axes leads to the identification of anisotropic volumetric compressibility. Loading of the materials with cubic symmetry of properties in the directions not coincided with the main directions (for example, 011) allows one to detect 75% cases of the auxetic single crystals (i.e. with negative Poisson’s ratio). In these cases, the negative volumetric compressibility has anisotropy, in contrast to the volumetric compressibility calculated along the crystallographic axes for cubic materials. Anisotropy of the volumetric compressibility leads to anisotropy of velocities of propagation of body waves. This paper considers several elastoplastic problems for a cubic material with different orientations of a coordinate system about its crystallographic axes. The behaviour of such a material under dynamic loads is modelled with an account of anisotropic bulk compressibility to provide the same anisotropy of bulk wave velocities in the elastic and plastic ranges and a uniform pressure function at the elastic-to-plastic strain transition. For each orientation of the coordinate system and respective planes, different values at the indicatrices of elastic constants are specified, and this specifies different deformation processes in cubic materials. Such an effect is demonstrated by solving three problems in three-dimensional (3D) statements approximating the following processes: (1) one-dimensional elastoplastic deformation in a thin target impacted by a thin plate; (2) uniform compression in a spherical body under pulsed hydrostatic pressure; and (3) 3D elastoplastic deformation in a cylindrical body striking a rigid target in view of anisotropic bulk compressibility. The problems were solved numerically using original programs based on the finite element method modified by GR Johnson for impact problems. Solving problems in a 3D formulation makes it possible to take into account the dependences of the direction of the elastic and plastic characteristics of the material, as well as the velocities of propagation of elastic and plastic waves from that direction. The simulation results suggest that for cubic materials, changing the orientation of two coordinate axes in a plane changes the strains along all three axes, including those perpendicular to this plane. It is concluded that anisotropic bulk compressibility in cubic materials should be allowed for by mathematical models of their elastic and plastic deformation. We demonstrate that the orientation of a computational coordinate system for cubic materials should be in those directions in which their deformation is analysed in each particular case.

Dispersion Diagram of Trigonal Piezoelectric Phononic Structures with Langasite Inclusions

The dispersion relation of elastic Bloch waves in 1-3 piezoelectric phononic structures (PPnSs) with Langasite (La3Ga5SiO14) inclusions in a polymeric matrix is reported. Langasite presents promising material properties, for instance good temperature behaviour, high piezoelectric coupling, low acoustic loss and high quality factor. Furthermore, Langasite belongs to the point group 32 and has a trigonal structure. Thus, the 2-D bulk wave propagation in periodic systems with Langasite inclusions cannot be decoupled into XY and Z modes. The improved plane wave expansion (IPWE) is used to obtain the dispersion diagram of the bulk Bloch waves in 1-3 PPnSs considering the classical elasticity theory and D3 symmetry. Full band gaps are obtained for a broad range of frequency. The piezoelectricity enhances significantly the band gap widths and opens up a narrow band gap in lower frequencies for a filling fraction of 0.5. This study should be useful for surface acoustic wave (SAW) filter and 1-3 piezocomposite transducer design using PPnSs with Langasite.