  An acoustic cloak envelopes an object so that sound incident from all
directions passes through and around the cloak as though the object were not
present. A theory of acoustic cloaking is developed using the transformation or
change-of-variables method for mapping the cloaked region to a point with
vanishing scattering strength. We show that the acoustical parameters in the
cloak must be anisotropic: either the mass density or the mechanical stiffness
or both. If the stiffness is isotropic, corresponding to a fluid with a single
bulk modulus, then the inertial density must be infinite at the inner surface
of the cloak. This requires an infinitely massive cloak. We show that perfect
cloaking can be achieved with finite mass through the use of anisotropic
stiffness. The generic class of anisotropic material required is known as a
pentamode material. If the transformation deformation gradient is symmetric
then the pentamode material parameters are explicit, otherwise its properties
depend on a stress like tensor which satisfies a static equilibrium equation.
For a given transformation mapping the material composition of the cloak is not
uniquely defined, but the phase and wave speeds of the pseudo-acoustic waves in
the cloak are unique. Examples are given from 2D and 3D.

Materials Science