Design of inhomogeneous pentamode metamaterials for minimization of scattering

Acoustic metamaterials use sub-wavelength, anisotropic, and inhomogeneous microstructures. Macroscopic properties can be related to the microstructure using homogenization theory Hassani and Hinton [Comput. Struct. 69, 719–738 (1998), which allows an analyst to confirm the extent to which a candidate metamaterial microstructure meets the requirements for a pentamode cloaking material. Norris [Proc. R. Soc. Ser. A, 464, 2411–2434 (2008)] presented a theory of transformation acoustics that enables the realization of inhomogeneous pentamode acoustic materials having anisotropic elastic tensors, isotropic density and finite mass. This theory describes the spatially varying material properties in terms of a mapping, which for separable geometries may be generated using a scalar function. This function, the constraints on its behavior implicit in the Norris theory, and the material equations constitute the defining relations for pentamode transformation acoustics. Previously, analytic work in transformation acoustics developed the material properties after having fixed a transformation. By reversing the process, we create a number of new families of pentamode cloaking materials. We validate the concept with three-dimensional explicit transient finite element simulations.