Christophe Aristégui

Optimal recovery of the elasticity tensor of general anisotropic materials from ultrasonic velocity data

An ultrasonic wave approach is presented for the optimal identification of the 21 independent elasticity constants of the most general linear homogeneous anisotropic elastic solid from wave speed measurements of obliquely incident ultrasonic bulk waves. Since the symmetry of acquisition planes is not taken into account, this inversion process is generalized to materials that do not possess three mutually orthogonal planes of symmetry. Minimization of an overdetermined system of nonlinear algebraic equations is solved by a constrained optimization method. Various classes of symmetry are considered. Several critical factors (initial guesses, scatter in experimental data) which can influence the accuracy of the elastic property reconstruction algorithm have been investigated by means of numerical examples that simulate in the best way a typical experiment. The sensitivity of the reconstruction algorithm to each identified elasticity constant is detected a posteriori by means of the estimation of a confidence...

Analysis of sound propagation in a fluid through a screen of scatterers

A multiple scattering analysis in a nonviscous fluid is developed in detail in order to predict the coherent sound motion in the presence of disordered heterogeneities, such as particles, fibers, bubbles, or contrast agents. Scatterers can be homogeneous, layered, shell-like with encapsulated liquids or gas, nonabsorbing, or absorbing, and can take a wide variety of shapes. A priori imposed limitations or physical assumptions are absent in the derivation, whether they concern the expected response of the fluid-scatterer mixture, the scatterer size relative to wavelength, or the scatterer concentration or the screen thickness. However, as in any multiple scattering formulation, a closure assumption is invoked. Closed-form results for the backscattered and forward-scattered wave motions on either side of the screen of scatterers are obtained. The fluid-scatterer mixture is shown to behave as an effective dissipative medium from the standpoint of the coherent motion. It is found that the effective medium is fully described once two parameters are determined: the effective wave number and the reflection coefficient for the associated half-space screen. Remarkably, both parameters depend only on the far-field scattering properties of a single scatterer.

Induced anisotropy and crack systems orientations of a ceramic matrix composite under off-principal axis loading

The effect of matrix microcracking on a ceramic matrix composite (CMC) is studied by means of an ultrasonic method. It provides the whole set of the stiffnesses of materials that possess any class of symmetry (including the most general anisotropy), and then the simultaneous identification of the angular parallax locating the higher symmetry coordinate system and the associated optimal stiffness tensor. The problem of damage-induced anisotropy, i.e., the orientation of the matrix microcracks comparative to the loading direction and to the material axes of the composite, may be treated without the limiting assumption that the material keeps its orthorhombic symmetry in an a priori known coordinate system. The induced anisotropy depends on the loading direction. If a tensile solicitation in one of the fiber directions induces damage modes that are parallel to one of the elasticity principal planes, a tensile solicitation along a non-principal direction creates microcracks with a predominant orientation that does not coincide with the elastic symmetry axes, and induces a fully anisotropic elastic degradation. The load-induced rotation of the elasticity principal coordinate system is emphasized. Finally, the assessment of the crack orientation, from the wave speed measurements, points out that the loading direction and the fiber directions both govern the direction of the crack growth.

Sharp acoustic multipolar-resonances in highly monodisperse emulsions

We report the achievement of highly monodisperse emulsions exhibiting about ten acoustic Mie resonances. Thanks to robotics, the effective acoustic properties of such strongly scattering media can be precisely targeted by means of the production of calibrated (random) liquid-droplets. Ultrasonic experiments are compared, with an excellent quantitative agreement, to theoretical predictions derived within the framework of the independent scattering approximation. The dependence of the sound speed and of the acoustic attenuation on both the size and the volume fraction of droplets is quantitatively examined for dilute and more concentrated emulsions, and is presented in a dimensionless way.

Soft porous silicone rubbers as key elements for the realization of acoustic metamaterials.

In this work, macroporous materials made of polydimethylsiloxane, a soft silicone rubber, are prepared using UV polymerization with an emulsion-templating procedure. The porosity of the final materials can be precisely controlled by adjusting the volume of the dispersed phase. We show that the porous structure of the materials is the template of the droplets of the initial emulsions. Mechanical tests show that the materials Youngs moduli decrease with the porosity of the materials. Acoustic measurements indicate that, in such a porous elastomeric matrix, the sound speed also decreases dramatically as soon as the porosity increases to attain values of as low as 80 m/s. The results are compared to earlier ones on silica aerogels and are interpreted within the framework of a simple theoretical approach. We show that the very low sound speed value is a consequence of the low value of the polymer shear modulus. This explains why such porous soft silicone rubbers are so efficient at playing the role of slow-soft resonators in acoustic metamaterials. Moreover, the fast rate of polymerization of such UV-curable fluid allows for a facile shaping of the final material as beads or rods in microfluidic devices.1.

Further results for antiplane scattering by a thin strip

A result, which does not appear to be available elsewhere, concerning the far-field scattering of antiplane waves by a single thin crack in an elastic solid is obtained in this letter. Specifically, the angular shape function is derived, with scattering coefficients expressed in terms of the crack-opening displacement. With this function, numerical values for effective speed and attenuation through a distribution of parallel cracks are obtained.

Optimal determination of the material symmetry axes and associated elasticity tensor from ultrasonic velocity data

A simultaneous identification of the angular parallax locating the higher symmetry coordinate system and the associated optimal stiffness tensor from wave speed measurements of obliquely ultrasonic bulk waves in an arbitrarily oriented coordinate system is presented. The property used in classifying a material with regard to its elastic symmetry is the existence and the number of planes of reflective or mirror symmetry. That leads to considering the problem of determining the symmetry class and the directions of the elements of symmetry. To consider the uncertainties of the experimental data, the wave speed measurements are only used to determine the symmetry frames and the optimal stiffness tensor. The proposed inverse propagation algorithm consists of minimizing a functional where the unknowns are the elasticity constants and the Euler angles between the geometric coordinate system and the frame of higher symmetry. Stability of the used least-square algorithm to the initial guesses and to the noise in t...

Impact of polydispersity on multipolar resonant scattering in emulsions

The influence of size polydispersity on the resonant acoustic properties of dilute emulsions, made of fluorinated-oil droplets, is quantitatively investigated. Ultrasound attenuation and dispersion measurements on various samples with controlled size polydispersities, ranging from 1% to 13%, are found to be in excellent agreement with predictions based on the independent scattering approximation. By relating the particle-size distribution of the synthesized emulsions to the quality factor of the predicted multipolar resonances, the number of observable acoustic resonances is shown to be imposed by the sample polydispersity. These results are briefly discussed into the context of metamaterials for which scattering resonances are central to their effective properties.

Soft porous silicone rubbers with ultra-low sound speeds in acoustic metamaterials

Soft porous silicone rubbers are demonstrated to exhibit extremely low sound speeds of tens of m/s for these dense materials, even for low porosities of the order of a few percent. Our ultrasonic experiments show a sudden drop of the longitudinal sound speed with the porosity, while the transverse sound speed remains constant. For such porous elastomeric materials, we propose simple analytical expressions for these two sound speeds, derived in the framework of Kuster and Toksöz, revealing an excellent agreement between the theoretical predictions and the experimental results for both longitudinal and shear waves. Acoustic attenuation measurements also complete the characterization of these soft porous materials.

Coherent acoustic response of a screen containing a random distribution of scatterers: Comparison between different approaches

Theoretical models underlying the ultrasonic study of suspensions and bubble swarms in liquids often rely on the concept of a coherent wave response, within which the given medium is viewed as an effective homogeneous medium. More specifically, the coherent response can be formulated in a straightforward manner via the effective wave number and the effective impedance. These in turn can be expressed through the actual material properties of the given scattering medium. The derivation of the effective wave number and impedance is the issue of a number of different approaches existing in the multiple-scattering theory. The present work deals with a coherent response of acoustic wave impinging on a screen of cylindrical inclusions randomly distributed in a fluid. The reflection and transmission coefficients have been expressed via the effective wave number and impedance that are provided by three different models due to Foldy, Waterman & Truell, and Linton & Martin. The obtained expressions have been analyzed with a view to illuminate what is the quantitative difference between those approaches as revealed in the coherent response, and how this difference depends on the basic parameters of the problem such as the frequency, the concentration of scatterers and their contrast relatively to the fluid matrix. Another aspect of this work is to compare the above analytical results with the numerical data. It has been obtained by means of a deterministic computational code which delivers the coherent wave field through averaging the outputs for various samplings of the positions of scatterers. Knowing this numerical benchmark allows us to specify the validity domains for each of the three analytical methods under study.