# Cloaking in-plane elastic waves with swiss rolls

## TL;DR

This paper introduces a novel cylindrical elastic cloak design using concentric swiss-roll inclusions that achieve partial in-plane shear wave cloaking at specific resonant frequencies by leveraging a unique geometric transform starting from Willis media.

## Contribution

The work presents a new elastic cloaking method based on a geometric transform from Willis media, breaking minor-symmetries and enabling shear wave cloaking with structured concentric layers.

## Key findings

- Achieves cloaking at resonant sub-wavelength frequencies
- Utilizes structured swiss-roll inclusions for effective medium design
- Breaks minor-symmetries in Willis equations to enable cloaking

## Abstract

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 Pendry's 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.