Cloaking in-plane elastic waves with swiss rolls

Abstract

We propose a design of cylindrical cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as Swiss rolls. The scaling factor between inclusions' sizes is according to Pendry's transform. Unlike the hitherto known situations, the present geometric transform starts from a Willis medium and further assumes that displacement fields u in original medium and u' in transformed medium remain unaffected (u' = u). This breaks the minor symmetries of the rank-4 and rank-3 tensors in theWillis equation that describe the transformed effective medium. We achieve some cloaking for a shear polarized source at specific, resonant sub-wavelength, frequencies, when it is located in close proximity to a clamped obstacle surrounded by the structured cloak. The structured medium approximating the effective medium allows for strong Willis coupling, notwithstanding potential chiral elastic effects, and thus mitigates roles ofWillis and Cosserat media in the achieved elastodynamic cloaking.