Metamaterials: supra\textit{supra}-classical dynamic homogenization

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material parameters that can be electronic, magnetic, acoustic, or elastic, and must adequately represent the wave interaction behaviour in the composite within desired frequency ranges. In some cases -- for example, the low frequency regime -- there exist various efficient ways by which effective material parameters for wave propagation in metamaterials may be found. However, the general problem of predicting frequency-dependent dynamic effective constants has remained unsolved. Here, we obtain novel mathematical expressions for the effective parameters of two-dimensional metamaterial systems valid at higher frequencies and wavelengths than previously possible. By way of an example, random configurations of cylindrical scatterers are considered, in various physical contexts: sound waves in a compressible fluid, anti-plane elastic waves, and electromagnetic waves. Our results point towards a paradigm shift in our understanding of these effective properties, and metamaterial designs with functionalities beyond the low-frequency regime are now open for innovation.Comment: 14 pages (including 4 figures and 1 table) in New Journal of Physics, 201

Scattering of antiplane elastic waves by two-dimensional periodic arrays of cracks

In the context of elastic wave propagation in damaged solids, an analytical approach for scattering of antiplane waves by two-dimensional periodic arrays of cracks is developed. Before considering the study of arrays of cracks, the scattering of an antiplane wave by a flat crack is first studied. Then, using the representation formula for the scattered displacement by a flat and by considering the periodicity condition of the crack-spacing, a boundary integral equation is obtained for the crack face displacement of the reference crack. Numerical results for the reflection and transmission coefficients are presented as functions of the crack-spacing, the frequency of excitation, and the angle of incidence. Finally, the propagation of antiplane waves by two-dimensional periodic arrays of cracks is studied. Despite the use of a finite number of linear arrays, one recognizes the effects of band-pass filtering or band rejection characteristics of the transmission spectra of a periodic medium. Effects due to a disorder in the periodicity are also analysed.Comment: 21 pages (including 9 figures), in Frenc

Three-dimensional ultrasonic colloidal crystals

Colloidal assembly represents a powerful method for the fabrication of functional materials. In this article, we describe how acoustic radiation forces can guide the assembly of colloidal particles into structures that serve as microscopic elements in novel acoustic metadevices or act as phononic crystals. Using a simple three-dimensional orthogonal system, we show that a diversity of colloidal structures with orthorhombic symmetry can be assembled with megahertz-frequency (MHz) standing pressure waves. These structures allow rapid tuning of acoustic properties and provide a new platform for dynamic metamaterial applications.Comment: 23 pages (including 12 figures

Sound propagation in a solid through a screen of cylindrical scatterers

The propagation of SH waves in a solid containing a screen of line-like scatterers is investigated. When the scatterers are uniformly distributed, the amplitudes of the coherent waves inside and outside the screen are evaluated in closed form. In the analysis, multiple scattering effects are taken into account within the context of a first-order approximation. A Global Closure Assumption is proposed, which yields an effective wavenumber identical to that of Waterman and Truell. The scatterers can be fibers of circular or elliptical cross-sections; they can also be two-dimensional cracks with slit-like or elliptical cross-sections. Specific analytical and numerical results are presented for flat cracks and empty cavities of circular cross-sections. In those two cases, figures are presented to illustrate the variations of the reflection and transmission coefficients as functions of frequency and of scatterer concentration. The crack and cavity results, respectively, are compared with those of earlier works

Consistance des modèles de symétrie des milieux effectifs utilisés en diffusion multiple

La modélisation de la propagation d’ondes dans les structures multifissurés est d’un intérêt majeur pour leur contrôle (non destructif) et leur dimensionnement. La question posée dans cette communication touche à la capacité de décrire la propagation d’ondes cohérentes (ou ondes moyennes) suivant toutes les directions (de l’espace) de tels milieux, à partir de la seule connaissance des propriétés effectives du milieu le long de ses directions principales macroscopiques (de symétries matérielles). L’importance de cette question est illustrée en considérant la propagation de l’onde de cisaillement antiplane cohérente et homogène, en incidence oblique sur une distribution aléatoire de fissures plates mutuellement parallèles. L’approximation de la lenteur de phase effective calculée à partir de l’équation de dispersion spécifique aux milieux orthotropes est alors comparée à des résultats de référence obtenus par une méthode directe de calcul considérant des ondes incidentes sur les fissures. Il s’avère que les raideurs effectives présentent dans l’équation de dispersion du modèle dit orthotrope (a priori en adéquation avec la symétrie élastique du milieu) doivent être dépendantes de la direction de propagation des ondes incidentes afin que celle-ci soit consistante avec les résultats de référence. La description matérielle macroscopique (justifiée dans le cas quasi-statique, ou de très grandes longueurs d’ondes) se trouve donc être à portée limitée et ne peut décrire correctement l’anisotropie de la propagation en régime fréquentiel intermédiaire. Finalement, le choix de la loi de Hooke comme loi constitutive du milieu homogène équivalent s’avère inadaptée pour ce régime fréquentiel

Haptics and directional audio using acoustic metasurfaces

The ability to control acoustic fields offers many possible applications in loudspeaker design, ultrasound imaging, medical therapy, and acoustic levitation. Sound waves are currently shaped using phased array systems, even though the complex electronics required are expensive and hinder widespread use. Here we show how to control, direct, and manipulate sound using 2-dimensional, planar, acoustic metasurfaces that require only one driving signal. This offers the advantages of ease of use and versatility over currently available phased arrays. We demonstrate the creation of a haptic sensation and steering of a beam produced by a parametric speaker. This simple, yet highly effective, method of creating single-beam manipulators could be introduced in medical or manufacturing applications

Modélisation de la propagation d'ondes élastiques antiplanes dans des milieux multifissurés

L’objectif de ce travail est de modéliser la propagation des ondes cohérentes antiplanes dans une distribution aléatoire et uniforme de fissures fermées ou ouvertes, parallèles ou aléatoirement orientées. Elles contiennent un fluide visqueux où leurs lèvres sont libres de contraintes. Les mécanismes de diffusion multiple entre fissures sont pris en compte. Une première étude porte sur la réponse d’une couche endommagée à faces parallèles, sollicitée à incidence normale. Les champs de déplacement cohérent siégeant dans les trois régions de l’espace sont déterminés. Par suite, la masse volumique et la rigidité effectives de la couche, vue homogène par l’onde cohérente, sont définies. Les cas d’une distribution de fissures à concentration variable et d’une onde de surface (de type Love) en présence d’une couche endommagée sur un substrat sain sont alors traités. Une dernière application concerne les populations de fissures visqueuses à tailles variables présentes dans la croûte terrestre.Abstrac