Cloaking in-plane elastic waves with swiss rolls

We propose a design of cylindrical elastic 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 Pendrys transform. Unlike the hitherto known situations, the present geometric transform starts from a Willis medium and further assumes that displacement fields ${bf u}$ in original medium and ${bf u}$ in transformed medium remain unaffected (${bf u}={bf u}$), and this breaks the minor-symmetries of the rank-4 and rank-3 tensors in the Willis equation that describes the transformed effective medium. We achieve some cloaking for a shear polarized source at specific, resonant sub-wavelength, frequencies, when it is located near a clamped obstacle surrounded by the structured cloak. Such an effective medium allows for strong Willis coupling [Quan et al., Physical Review Letters {bf 120}(25), 254301 (2018)], notwithstanding potential chiral elastic effects [Frenzel et al., Science {bf 358}(6366), 1072 (2017)], and thus mitigates roles of Willis and Cosserat media in the achieved elastodynamic cloaking.