Olivier Bou Matar

A two-dimensional pseudospectral model for time reversal and nonlinear elastic wave spectroscopy

One way to characterize metallic materials in the presence of defects like dislocation networks is to measure their large dynamic nonlinear elastic response. In this numerical study, a new method combining the nonlinear elastic wave spectroscopy (NEWS) method with a time reversal (TR) process is proposed. This method, called NEWS-TR, uses nonlinear analysis as a pretreatment of time reversal and then consists of retrofocusing only nonlinear components on the defect position. A two-dimensional pseudospectral time domain algorithm is developed here to validate the NEWS-TR method as a potential technique for damage location. Hysteretic nonlinear behavior of the materials being studied is introduced using the Preisach-Mayergoyz model. Moreover, in order to extend this solver in two dimensions, the Kelvin notation is used to modify the elastic coefficient tensor. Simulations performed on a metallic sample show the feasibility and value of the NEWS-TR methodology for microdamage imaging. Retrofocusing quality depends on different parameters such as the filtering method used to keep only nonlinear components and the nonlinear effect measured. In harmonic generation, pulse inversion filtering seems to be a more appropriate filtering method than classical harmonic filtering for most defect positions, mainly because of its ability to filter all fundamental components.

Convolutional perfectly matched layer for elastic second-order wave equation

In this work, a method is presented to extend the convolutional perfectly matched layer (C-PML) to simulate acoustic wave propagation in elastic media with a second-order equation formulation. This non-physical layer is used at the computational edge of a finite element method algorithm in frequency domain, and a pseudo-spectral algorithm in time domain, as an absorbing boundary condition (ABC) to truncate unbounded media. Numerical results show that the C-PML ABC attenuates the outgoing surface waves more effectively than classical PML ABC as proposed by Berenger [J. Comput. Phys. 114, 195-200 (1994)] for electromagnetic waves in the case of oblique incidence, where the PML method suffers from large spurious reflections. Moreover, a modification of the proposed C-PML formulation is also discussed in order to stabilize the absorbing layer in anisotropic solids where numerical instabilities can appear.

Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Greens function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.

Application of nonlinear phenomena induced by focused ultrasound to bone imaging.

A tissue deformability image is obtained with the vibroacoustography imaging method using mechanical low-frequency (LF) excitation. This ultrasonic excitation is created locally by means of a focused annular array emitting two primary beams at two close frequencies, f(1) and f(2) (f(2) = f(1) + f(LF)). The LF acoustic emission resulting from the vibration of the medium is detected by a sensitive hydrophone and then used to form the image. This noninvasive imaging method was demonstrated in this study to be suitable for bone imaging, with x and y transverse resolutions less than 300 micro m. Two bone sites susceptible to demineralization were tested: the calcaneus and the neck of the femur. The vibroacoustic method provides valuable ultrasonic images regarding the structure and the elastic properties of bone tissue. Correlation was made between vibroacoustic bone images, performed in vitro, and images acquired by other imaging methods (i.e., bone ultrasound attenuation and x-ray computerized tomography (CT)). Moreover, the amplitudes of vibroacoustic signals radiating from phosphocalcic ceramic samples (bone substitute) of different porosity were evaluated. The good correlation between these results and the description of our images and the quality of vibroacoustic images indicate that bone decalcification could be detected using vibroacoustography.

Low power sessile droplets actuation via modulated surface acoustic waves

Low power actuation of sessile droplets is of primary interest for portable or hybrid lab-on-a-chip and harmless manipulation of biofluids. In this paper, we show that the acoustic power required to move or deform droplets via surface acoustic waves can be substantially reduced through the forcing of the drops inertio-capillary modes of vibrations. Indeed, harmonic, superharmonic, and subharmonic (parametric) excitation of these modes are observed when the high frequency acoustic signal (19.5 MHz) is modulated around Rayleigh-Lamb inertio-capillary frequencies. This resonant behavior results in larger oscillations and quicker motion of the drops than in the non-modulated case.

Two-dimensional axisymmetric numerical simulation of supercritical phase conjugation of ultrasound in active solid media

In the present study a two-dimensional axisymmetric numerical model is developed for supercritical parametric phase conjugation of ultrasound in a solid active element of cylindrical shape and finite length. The pseudospectral time domain algorithm (PSTD) is used owing to its efficiency to model large-scale problems. PSTD solves elastic wave equation in time-dependent heterogeneous isotropic and axisymmetric anisotropic solids using FFTs for high order approximation of the spatial differential operator on staggered grid, and a fourth-order Adams–Bashforth time integrator. In order to truncate the computational domain absorbing boundary conditions are introduced with complex frequency shifted perfectly matched layers. This procedure is highly effective at absorbing signals of long time-signature. The free surface of the active ceramic rod is introduced through the method of images. A systematic study of the influence of lateral limitations of the active medium on parametric wave phase conjugation of sound ...

A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation

A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lambs problem and plane wave nonlinear propagation.

Two-dimensional simulation of the single-sided air-coupled ultrasonic pitch-catch technique for non-destructive testing.

Non-contact air-coupled ultrasonic inspection of materials using single-sided access offers interesting possibilities for the development of in-line non-destructive testing (NDT) systems. This contribution reports observations and simulations obtained from a single-sided air-coupled pitch-catch configuration. The pitch-catch technique involves a set-up in which transmitter and receiver are located at the same side of the test object. Sound waves, reflected once or multiple times from the back-wall of the object or refracted by a discontinuity, are recorded and analyzed for visualization. The feasibility of the technique is demonstrated, experimentally, in the case of artificial defects in aluminium samples. Depending on the configuration one or more ultrasonic images of the defect can be observed, their number and relative position containing information about the location of the defect. The experiments are simulated using two distinctive methods. The first simulation is based on a ray tracing (shadow) approach, the second method uses a spectral solution implemented within COMSOL. Both simulation methods allow simple prediction of the response images in experimental conditions with supplementary levels of complexity, which will assist the development and optimization of online inspection techniques.

Theoretical and experimental study of the influence of the particle size distribution on acoustic wave properties of strongly inhomogeneous media

The ultrasonic method is particularly suitable to characterize diffusive media, as acoustic properties (velocity and attenuation) are related to the properties and concentrations of the homogeneous phase and scatterers. Thus, ultrasonic characterization can be useful in the study of sedimentation or flocculation processes, in concentration measurements, and granulometry evaluation. Many models have been developed for media where particles are very small compared to the incident wavelength. When the diameter of the particles is close to the wavelength, multiple-scattering theories have to be used to describe the propagation of waves. In this paper, the case where the ratio of wavelength to scatterer size is around unity is studied. First, the particle size distribution is taken into account in two types of multiple-scattering theories based on the effective field approximation or on the quasicrystalline approximation and theoretical results are produced. The T-matrix formalism has been used to calculate the amplitude of the wave scattered by a single sphere. The calculation of the complex wave number in the effective medium has been implemented, using in particular the Percus-Yevick equation as a spatial pair-correlation function between scatterers, and a normal particle-size distribution. The influence of these parameters is discussed. Finally, attenuation and phase velocity measurements are performed in moving suspensions of acrylic spheres in ethylene glycol, at various concentrations and for different particle-size distributions. A good agreement between the theoretical results and the measurements is found for both velocity and attenuation. These results show that the size distribution is a critical parameter to understand velocity and attenuation behavior as function of frequency and volume fraction.

Legendre and Laguerre polynomial approach for modeling of wave propagation in layered magneto-electro-elastic media

A numerical method to compute propagation constants and mode shapes of elastic waves in layered piezoelectric-piezomagnetic composites, potentially deposited on a substrate, is described. The basic feature of the method is the expansion of particle displacement, stress fields, electric and magnetic potentials in each layer on different polynomial bases: Legendre for a layer of finite thickness and Laguerre for the semi-infinite substrate. The exponential convergence rate of the method for propagation of Love waves is numerically verified. The main advantage of the method is to directly determine complex wave numbers for a given frequency via a matricial eigenvalue problem, in a way that no transcendental equation has to be solved. Results are presented and the method is discussed.