Achieving control of in-plane elastic waves

We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with 16 spatially varying entries which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [Milton et al., New J. Phys. 8, 248 (2006)]. We numerically check that clamped and freely vibrating obstacles located inside the neutral region are cloaked disrespectful of the frequency and the polarization of an incoming elastic wave. Recently, significant progress has been made on the control of acoustic and electromagnetic waves. Transformation based solutions to the conductivity and Maxwell’s equations in curvilinear coordinate systems, subsequently reported by Greenleaf et al. [1] and then by Pendry et al. [2] and Leonhardt [3], enable one to bend electromagnetic waves around arbitrarily sized and shaped solids. More precisely, the electromagnetic invisibility cloak is a metamaterial which maps a concealment region into a surrounding shell: as a result of the coordinate transformation the permittivity and permeability are strongly heterogeneous and anisotropic within the cloak, yet fulfilling impedance matching with the surrounding vacuum. The cloak thus neither scatter waves nor induces a shadow in the transmitted field. In [4], a cylindrical electromagnetic cloak constructed using specially designed concentric arrays of split ring resonators, was shown to conceal a copper cylinder around