Three-dimensional pentamode acoustic metamaterials with hexagonal unit cells.

Acoustic cloaking is an important application of acoustic metamaterials. Pentamode acoustic cloaks have isotropic mass density and anisotropic stiffness. A different kind of pentamode material is proposed in this paper. It is composed of three-dimensional hexagonal unit cells built with double-cone structures. The structure is amenable for creating spherical pentamode geometries, which might be used for acoustic cloaking. The band structures show that there are band gaps for shear waves, where only compressional waves exist. The effective compressional wave velocities are calculated from the band structures for various parameters. The effective properties can be varied by changing the parameters independently. High anisotropy and large variation of effective properties are demonstrated, suggesting good potential for acoustic cloaking. The geometry of the unit cell can be designed to give the appropriate properties required for cloaking.