Negative refraction of elastic waves has been studied and experimentally demonstrated in three-and two-dimensional phononic crystals, but Bragg scattering is impractical for low-frequency wave control because of the need to scale the structures to manageable sizes. Here we present an elastic metamaterial with chiral microstructure made of a single-phase solid material that aims to achieve subwavelength negative refraction of elastic waves. Both negative effective mass density and modulus are observed owing to simultaneous translational and rotational resonances. We experimentally demonstrate negative refraction of the longitudinal elastic wave at the deep-subwavelength scale in the metamaterial fabricated in a stainless steel plate. The experimental measurements are in good agreement with numerical simulations. Moreover, wave mode conversion related with negative refraction is revealed and discussed. The proposed elastic metamaterial may thus be used as a flat lens for elastic wave focusing.

In this letter, an elastic metamaterial which exhibits simultaneously negative effective mass density and bulk modulus is presented with a single unit structure made of solid materials. The double-negative properties are achieved through a chiral microstructure that is capable of producing simultaneous translational and rotational resonances. The negative effective mass density and effective bulk modulus are numerically determined and confirmed by the analysis of wave propagation. The left-handed wave propagation property of this metamaterial is demonstrated by the negative refraction of acoustic waves.

Performance of classic sound absorbing materials strictly depends on their thickness, with a minimum of one-quarter wavelength to reach full sound absorption. In this paper, we report ultrathin sound absorbing panels that completely absorb sound energy with a thickness around one percent of wavelength. The strategy is to bend and coil up quarter-wavelength sound damping tubes into 2D coplanar ones, and embed them into a matrix to form sound absorbing panel. Samples have been designed and fabricated by 3D printing. Efficacies of sound absorption by these panels were validated through good agreement between theoretical analysis and experimental measurements.

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a b s t r a c tIn continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However, when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral. Therefore, influence of the chiral effect cannot be properly characterized by existing theories for 2D chiral solids. To circumvent this difficulty, based on reinterpretation of isotropic tensors in the 2D case, we propose a continuum theory to model the chiral effect for 2D isotropic chiral solids. A single material parameter related to chirality is introduced to characterize the coupling between the bulk deformation and the internal rotation, which is a fundamental feature of 2D chiral solids. Coherently, the proposed continuum theory is applied for the homogenization of a triangular chiral lattice, from which the effective material constants of the lattice are analytically determined. The unique behavior in the chiral lattice is demonstrated through the analyses of a static tension problem and a plane wave propagation problem. The results, which cannot be predicted by the non-chiral model, are verified by the exact solution of the discrete model.

In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplace's equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the spherical and elliptical cylindrical cloaks are derived based on the analytical solutions of the Laplace's equation. For cloaks with irregular shapes, the material parameters of the transformation medium are determined numerically by solving the Laplace's equation. Full-wave simulations based on the Maxwell's equations validate the designed cloaks. The proposed method can be easily extended to design other transformation materials for electromagnetic and acoustic wave phenomena.

A unified analytic model for effective mass density, effective bulk modulus, and effective shear modulus is presented for elastic metamaterials composed of coated spheres embedded in a host matrix. The effective material properties are derived directly from the averages of local momentum, stress, and strain defined in a single doubly coated sphere. It is shown that the effective material parameters predicted by the proposed model are in excellent agreements with the coherent-potential approximation results at low filling fractions where the anisotropy of periodic structures can be neglected for elastic waves. The advantage of the proposed method is that it can reveal clearly the physical mechanism for negative effective material parameters induced by the resonant effect. It is found that negative effective mass density is induced by negative total momentum of the composite for a positive momentum excitation. Negative effective bulk modulus appears for composites with an increasing ͑decreasing͒ total volume under a compressive ͑tensile͒ stress. Negative effective shear modulus describes composites with axisymmetric deformation under an opposite axisymmetric loading. Numerical examples are also given to illustrate these mechanisms. These findings may be useful in design of elastic metamaterials.