Transparency effect induced by elastic metamaterials

In the quasi-static limit, it is shown that the neutral inclusion concept can be applied to predict the transparency phenomenon. The transparency designs for a coated ellipsoid for electromagnetic wave and a multilayered sphere for acoustic wave with metamaterials have been proposed. In this paper, we will show how to cloak a solid object with elastic wave metamaterial, where the shear wave in the system is nontrivial. Based on the Mie theory, it is shown that the effective bulk modulus, mass density, and shear modulus of the assemblage made of the coated spheres dominate the zero, the first and the second order scattering coefficients of one coated sphere, respectively. So letting the first three scattering coefficients vanish, the isotropic coated metamaterial can be determined in order to make a spherical object transparent for elastic wave, this again corresponds to the neutral inclusion concept.