Numerical simulation of laser-generated ultrasound in non-metallic material by the finite element method

The use of a pulsed laser for the generation of the elastic waves in non-metallic materials in the thermoelastic regime is investigated by using finite element method (FEM), taking into account not only thermal diffusion and the finite spatial and temporal shape of the laser pulse, but also optical penetration and the temperature dependence of material properties. The optimum finite element model is established based on analysis of two important parameters, meshing size and time step, and the stability of solution. Temperature distributions and temperature gradient fields in non-metallic material for different time steps are obtained, this temperature field is equivalent to a bulk force source to generate ultrasonic wave. The laser-generated ultrasound waveforms at the epicenter and surface acoustic waveforms (SAWs) are obtained and the influence of optical penetration into the material on the temperature field and the ultrasound waveforms are analyzed. The numerical results indicate that the heat penetration into non-metallic material is caused mainly by the optical penetration, and the ultrasound waveforms, especially the shape of the precursor, are strongly dependent on the optical penetration depth into non-metallic material.     

Thermal and mechanical finite element modeling of laser-generated ultrasound in coating–substrate system

Thermal and mechanical finite element modeling of laser-generated ultrasound in coating–substrate system is presented, which entails a numerical formulation for the transient responses in terms of the characteristics of the source that originated the waves in the thermoelastic regime. The formulation takes into account the temperature dependence of the material parameters and thermal diffusion from the source. Numerical results show that the temperature gradient field is equivalent to the body force source, namely, vertical forces propagate downward and horizontal forces outward in the specimen. Waveforms at the epicenter present fast oscillations immediately after the precursor, which are produced by multiple reflections of the longitudinal in the coating, the thickness of the coating has remarkable influence on the waveforms at the epicenter.     

Numerical simulation of laser-generated surface acoustic waves in the transparent coating on a substrate by the finite element method

The optimum finite element model in the system consisting of a transparent coating and an opaque substrate is established based on the analysis of two important parameters: meshing size and time step, and the stability of solution. Taking into account the temperature dependence of material properties, the transient temperature and temperature gradient field are obtained. According to the thermoelastic theory, this temperature gradient field can be taken as a buried bulk source to generate ultrasonic wave. The surface acoustic waves (SAWs) are obtained. The influence of the coating thickness on the SAWs is analyzed. The model provides a useful tool for the determination of modes which are generated by a laser source in transparent coating on opaque substrate. The surface skimming longitudinal wave exists for the multiple oscillations and it charges from unipolar waveforms to dipolar.     

Numerical investigation of ultrasound reflection and backscatter measurements in cancellous bone on various receiving areas

In this study, new ultrasound reflection and backscatter measurements in cancellous bone using a membrane-type hydrophone are proposed. A membrane hydrophone made of a piezoelectric polymer film mounted on an annular frame allows an incident ultrasound wave to pass through its aperture because it has no backing material. Therefore, in measurements using the membrane hydrophone, the receiving area could be located independently from the transmitting area. In addition, the size and shape of the receiving area, which corresponded to those of the electrode deposited on the piezoelectric film, could be arranged in various ways. To investigate the validity of the proposed measurements, before bench-top experiments, the reflected and backscattered waves from cancellous bone were numerically simulated using a finite-difference time-domain method. The reflection and backscatter parameters were measured on various receiving areas, and their correlation coefficients with the structural parameters in the cancellous bone were derived. The simulated results suggested that appropriate receiving areas for the reflection and backscatter measurements could exist and that the proposed measurements could be more effective for evaluating bone properties than conventional measurements.     

超声诊断骨质疏松症中松质骨的模型

骨质疏松症(OP)是老龄化社会中影响健康的一个重要问题，超声技术已成为诊断骨质疏松症的一种常用方法。文中综述了近年来用超声诊断骨质疏松症中松质骨模型研究的进展，对棒状模型、流体多孔介质模型(Biot理论)和层状模型(schoenberg理论)进行了分析和讨论，指出了各理论模型存在的缺陷，对下一步的研究工作提出了建议。     

Hierarchical modeling of diffusive transport through nanochannels by coupling molecular dynamics with finite element method

We present a successful hierarchical modeling approach which accounts for interface effects on diffusivity, ignored in classical continuum theories. A molecular dynamics derived diffusivity scaling scheme is incorporated into a finite element method to model transport through a nanochannel. In a 5 nm nanochannel, the approach predicts 2.2 times slower mass release than predicted by Fick’s law by comparing time spent to release 90% of mass. The scheme was validated by predicting experimental glucose diffusion through a nanofluidic membrane with a correlation coefficient of 0.999. Comparison with experiments through a nanofluidic membrane showed interface effects to be crucial. We show robustness of our discrete continuum model in addressing complex diffusion phenomena in biomedical and engineering applications by providing flexible hierarchical coupling of molecular scale effects and preserving computational finite element method speed.     

Numerical treatment of acoustic problems with the smoothed finite element method

We incorporated a cell-wise acoustic pressure gradient smoothing operation into the standard compatible finite element method and extended the smoothed finite element method (SFEM) for 2D acoustic problems. This enhancement was especially useful for dealing with the problem of an arbitrary shape with violent distortion elements. In this method, the domain integrals that involve shape function gradients can be converted into boundary integrals that involve only shape functions. Restrictions on the shape elements can be removed, and the problem domain can be discretized in more flexible ways. Numerical results showed that the proposed method achieved more accurate results and higher convergence rates than the corresponding finite element methods, even for violently distorted meshes. The most promising feature of SFEM is its insensitivity to mesh distortion. The superiority of the method is remarkable, especially when solving problems that have high wave numbers. Hence, SFEM can be beneficially applied in solving two-dimensional acoustic problems with severely distorted elements, which, in practice, have more foreground than regularity mesh.     

Two-wave behavior under various conditions of transition area from cancellous bone to cortical bone

The two-wave phenomenon, the wave separation of a single ultrasonic pulse in cancellous bone, is expected to be a useful tool for the diagnosis of osteoporosis. However, because actual bone has a complicated structure, precise studies on the effect of transition conditions between cortical and cancellous parts are required. This study investigated how the transition condition influenced the two-wave generation using three-dimensional X-ray CT images of an equine radius and a three-dimensional simulation technique. As a result, any changes in the boundary between cortical part and trabecular part, which gives the actual complex structure of bone, did not eliminate the generation of either the primary wave or the secondary wave at least in the condition of clear trabecular alignment. The results led us to the possibility of using the two-wave phenomenon in a diagnostic system for osteoporosis in cases of a complex boundary.     

Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound

A novel semi-empirical scattering model of trabecular bone facilitating its characterization and allowing optimization of the interrogating pulse-echo transducer performance was developed. The model accounts for spatial density distribution of the trabeculae and includes measurement conditions such as pressure–time waveform of the probing ultrasound wave, the emitted field structure, and the transfer function and limited bandwidth of the acoustic source operating in pulse-echo mode. These measurement conditions are of importance as they modify the scattered echoes, which in turn are linked to the micro-architecture of the bone. The bone was modeled by a random distribution of long and thin cylindrical scatterers having randomly varying diameters and mechanical properties, and oriented perpendicularly to the ultrasound beam axis. To mimic clinically encountered conditions the relevant empirical data obtained at 1 MHz were input to the model. The data included pulse-echo source pressure field distribution in the focal zone and the above mentioned transfer function. With these data the model allowed frequency dependent backscattering coefficient of the simulated bone structure and its statistical properties to be determined. The results obtained indicated that the computer simulation is of particular relevance in studying scattering properties of the cancellous bone and holds promise as a tool to determine the relationship between the physical dimensions and shape of the scatterers and for monitoring of osteoporosis. The results of simulations also indicated that the new bone model proposed is well suited to mimic clinically relevant conditions. In contrast to the existing bone models, which usually assume scatterers to be randomly distributed as infinitely long identical cylinders with a cross-section much smaller than the probing ultrasound wave, the new model includes two populations of scatterers having different physical dimensions and also allows the mechanical properties of the scatterers to be varied.     

A coupled edge-/face-based smoothed finite element method for structural-acoustic problems

The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems.     

Reducing temperature influence on dry quantitative ultrasound bone assessment with constant temperature control

Nowadays, ultrasonic bone assessment is increasingly being used to assess bone status. Therefore, the purpose of this study was to enhance the precision of ultrasonic bone assessment by reducing the influence of temperature in a dry, gel coupled transducer system. A warm airflow generator was designed to make the measurement temperature constant (35 ± 1 °C). Thirty people were recruited for the evaluation of in-vivo performance. The short-term precision was performed 10 times with repositioning during a consecutive measurement session within 20 min. It was expressed as root-mean square average of coefficient of variation, which is abbreviated for CV_RMS. The CV_RMS was 3.84% for broadband ultrasound attenuation, and 0.30% for speed of sound. The Pearson correlations between gel coupled transducer system and dual energy X-ray absorptiometry (DEXA) were 0.808 (p < 0.001) for broadband ultrasound attenuation, and 0.586 (p < 0.005) for speed of sound. The result showed the high performance of reproducibility and the significant (p < 0.005) correlations with DEXA in the dry, gel coupled transducer system.     

Least-squares finite element method for radiation heat transfer in graded index medium

To avoid the complicated and time-consuming computation of curved ray trajectories, a least-squares finite element method based on discrete ordinate equation is extended to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Four cases of radiative heat transfer are examined to verify this least-squares finite element method. Linear and nonlinear graded index are considered. The predicted dimensionless net radiative heat fluxes are determined by the least-squares finite element method and compared with the results obtained by other methods. The results show that the least-squares finite element method is stable and has a good accuracy in solving the multi-dimensional radiative transfer problem in a semitransparent graded index medium, while the Galerkin finite element method sometimes suffers from nonphysical oscillations.     

A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.     

Determination of propagation constants in a Ti:LiNbO3 optical waveguide by using finite element and variational methods

The finite element and variational methods are used to determine the propagation constants in a titanium indiffused lithium niobate waveguide with the reconstructed refractive index profile (in depth) from the near field measurements. A subsequent second diffusion of magnesium affects the shape of the calculated electric field and we have defined an effective depth of the profile.     

Estimation of ultrasonic attenuation in a bone using coded excitation

This paper describes a novel approach to estimate broadband ultrasound attenuation (BUA) in a bone structure in human in vivo using coded excitation. BUA is an accepted indicator for assessment of osteoporosis. In the tested approach a coded acoustic signal is emitted and then the received echoes are compressed into brief, high amplitude pulses making use of matched filters and correlation receivers. In this way the acoustic peak pressure amplitude probing the tissue can be markedly decreased whereas the average transmitted intensity increases proportionally to the length of the code. This paper examines the properties of three different transmission schemes, based on Barker code, chirp and Golay code. The system designed is capable of generating 16 bits complementary Golay code (CGC), linear frequency modulated (LFM) chirp and 13-bit Barker code (BC) at 0.5 and 1 MHz center frequencies. Both in vivo data acquired from healthy heel bones and in vitro data obtained from human calcaneus were examined and the comparison between the results using coded excitation and two cycles sine burst is presented. It is shown that CGC system allows the effective range of frequencies employed in the measurement of broadband acoustic energy attenuation in the trabecular bone to be doubled in comparison to the standard 0.5 MHz pulse transmission. The algorithm used to calculate the pairs of Golay sequences of the different length, which provide the temporal side-lobe cancellation is also presented. Current efforts are focused on adapting the system developed for operation in pulse-echo mode; this would allow examination and diagnosis of bones with limited access such as hip bone.     

Simulation on laser-induced surface acoustic wave on isotropic cylinders by finite element method

Based on the thermoelastic theory, a finite element model is developed to simulate the process of laser inducing ultrasonic field in isotropic cylinders, which can take the temperature dependence of thermal parameters into account. Using the finite element model, we have simulated the ultrasonic fields induced by a pulse laser line source impacting on the generatrix of aluminum cylinders with different diameters. And the intact waveforms of surface acoustic wave (SAW including cylindrical Rayleigh and Whispering gallery (WG) modes) are presented, which are in very good agreement with the calculated and experimental waveforms in other literatures. Furthermore, the dispersion properties of cylindrical Rayleigh waves are analyzed by the method of phase spectral analysis, and the results show that with the increasing frequency, the phase velocity of cylindrical Rayleigh wave rapidly increases to the maximum value, and then gradually decreases to that of plane Rayleigh wave. With the diameter of cylinder decreasing, the maximum value of phase velocity and the corresponding frequency increase.     

Finite element method for modeling radiative transfer in semitransparent graded index cylindrical medium

Both Galerkin finite element method (GFEM) and least squares finite element method (LSFEM) are developed and their performances are compared for solving the radiative transfer equation of graded index medium in cylindrical coordinate system (RTEGC). The angular redistribution term of the RTEGC is discretized by finite difference approach and after angular discretization the RTEGC is formulated into a discrete-ordinates form, which is then discretized based on Galerkin or least squares finite element approach. To overcome the RTEGC-led numerical singularity at the origin of cylindrical coordinate system, a pole condition is proposed as a special mathematical boundary condition. Compared with the GFEM, the LSFEM has very good numerical properties and can effectively mitigate the nonphysical oscillation appeared in the GFEM solutions. Various problems of both axisymmetry and nonaxisymmetry, and with medium of uniform refractive index distribution or graded refractive index distribution are tested. The results show that both the finite element approaches have good accuracy to predict the radiative heat transfer in semitransparent graded index cylindrical medium, while the LSFEM has better numerical stability.     

Finite element method for the two-dimensional atmospheric radiative transfer

The finite element method is applied to the solution of the two-dimensional atmospheric radiative transfer. The analysis is mainly focussed on the derivation of the cell or element equation. The Galerkin method and several hybrid methods using the integral and finite difference form of the radiative transfer equation are employed to obtain the cell equation. The assembled system of equations relating the radiances at the lower and upper boundary of the domain is solved by a direct method.     

Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

Multi-chamber perforated resonator (MCPR) is a kind of typical silencer element which can both attenuate broadband noise and satisfy specific installation requirements. The one-dimensional transfer matrix method (TMM) and finite element method (FEM) are widely used to predict the transmission loss of the resonators. This paper mainly focuses on the comparison between 1D TMM and FEM in which detailed perforation modeling is applied for the acoustic modeling of MCPRs. Five resonators with different acoustic attenuation frequency ranges are built for simulation and test. In order to verify the results of the above methods, a transmission loss test facility is designed based on two-load method. Through adjusting the distance between microphones, the facility’s effective measurement frequency can be changed. The results show that despite of the complex modeling and calculation, FEM with detailed perforation modeling shows good consistency with test results in both frequency and amplitude within entire frequency range. In comparison, TMM is limited by the cut-off frequency when calculating transmission losses. Besides, accuracy of TMM in low frequency range is also affected by perforation conditions. However, TMM is time-saving in calculation and structure optimization. In MCPRs’ development process, TMM can be used to quickly design and optimize structure parameters while FEM can be used to verify the acoustic performance before prototyping.     

Identification of the piezoelectric material coefficients using the finite element method with an asymptotic waveform evaluation

A rapid identification of the piezoelectric material constants for a piezoelectric transducer is proposed. The validity of a three-dimensional finite element routine was confirmed experimentally. The asymptotic waveform evaluation (AWE) was adopted for a fast frequency sweep of the finite element analysis. The three-dimensional finite element method with an AWE and a design sensitivity method was used for a material inversion scheme of piezoelectric transducers. In order to confirm the inversion routine of the material constants, the mechanical displacements, which mean the mode shape, were calculated along the vertical and lateral position of the sample transducer.