We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves.\ud The cloak is characterized by a rank 4 elasticity tensor with spatially varying entries, which are\ud deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [G. W. Milton et al., N. J. Phys. 8, 248 (2006)]. The validity\ud of our approach is confirmed by comparison of the analytic Green’s function in homogeneous\ud isotropic elastic space against full-wave finite element computations in a heterogeneous anisotropic\ud elastic region surrounded by perfectly matched layers

We describe the first practical realization of a cylindrical cloak for linear surface liquid waves. This structured metamaterial bends surface waves radiated by a closely located acoustic source over a finite interval of Hertz frequencies. We demonstrate theoretically its unique mechanism using homogenization theory: the cloak behaves as an effective anisotropic fluid characterized by a diagonal stress tensor in a cylindrical basis. A low azimuthal viscosity is achieved, where the fluid flows most rapidly. Numerical simulations demonstrate that the homogenized cloak behaves like the actual structured cloak. We experimentally analyze the decreased backscattering of a fluid with low viscosity and finite density (methoxynonafluorobutane) from a cylindrical rigid obstacle surrounded by the cloak when it is located a couple of wavelengths away from the acoustic source.

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We propose a type of locally resonant structure involving arrays of structured coated inclusions. The coating consists of a structural interface with beams inclined at a certain angle. Such an elastic metamaterial supports tunable low-frequency stop bands associated with localized rotational modes that can be used in the design of filtering, reflecting, and focusing devices. Asymptotic estimates for resonant frequencies are in good agreement with finite element computations and can be used as a design tool to tune stop band changing relative inclinations, number, and cross section of the beams. Inertial resonators with inclined ligaments allow for anomalous dispersion (negative group velocity) to occur in the pressure acoustic band and this leads to the physics of negative refraction, whereby a point force located above a finite array of resonators is imaged underneath for a given polarization. We finally observe that for a periodic macrocell of the former inertial resonators with one defect in the middle, an elastic trapped mode exists within a high-frequency stop band. The latter design could be used in the enhancement of light and sound interactions in photonic crystal fiber preforms

Piccolroaz, A; Mishuris, G; Movchan AB. Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks. Journal of the Mechanics and Physics of Solids. 2009, 57(9), 1657-1682In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.Peer reviewe