Special transformations for pentamode acoustic cloaking

The acoustic cloaking theory of Norris [Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008)] permits considerable freedom in choosing the transformation f from physical to virtual space. The standard process for defining cloak materials is to first define f and then evaluate whether the materials are practically realizable. In this paper, this process is inverted by defining desirable material properties and then deriving the appropriate transformations which guarantee the cloaking effect. Transformations are derived which result in acoustic cloaks with special properties such as (1) constant density, (2) constant radial stiffness, (3) constant tangential stiffness, (4) power-law density, (5) power-law radial stiffness, (6) power-law tangential stiffness, and (7) minimal elastic anisotropy.