Controlling solid elastic waves with spherical cloaks

We propose a cloak for coupled shear and pressure waves in solids. Its elastic properties are deduced from a geometric transform that retains the form of Navier equations. The spherical shell is made of an anisotropic and heterogeneous medium described by an elasticity tensor ℂ ' (without the minor symmetries), which has 21 non-zero spatially varying coefficients in spherical coordinates. Although some entries of ℂ ', e.g., some with a radial subscript, and the density (a scalar radial function) vanish on the inner boundary of the cloak, this metamaterial exhibits less singularities than its cylindrical counterpart studied in [M. Brun, S. Guenneau, and A. B. Movchan, Appl. Phys. Lett. 94, 061903 (2009).] In the latter work, ℂ ' suffered some infinite entries, unlike in our case. Finite element computations confirm that elastic waves are smoothly bent around a spherical void.