Achaoui Younes, Diatta André, Kadic Muamer, Guenneau Sébastien
Institut FEMTO-ST, UMR 6174, CNRS, Université de Bourgogne Franche-Comté, 25000 Besanco̧n, France.
Aix Marseille University, CNRS, Centrale Marseille, Institut Fresnel, 13013 Marseille, France.
Materials (Basel). 2020 Jan 17;13(2):449. doi: 10.3390/ma13020449.
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 the Willis 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 of Willis and Cosserat media in the achieved elastodynamic cloaking.
我们提出了一种用于耦合面内剪切波的圆柱形隐身衣设计，它由同心层的亚波长共振无应力夹杂物组成，这些夹杂物形状为瑞士卷。夹杂物尺寸之间的缩放因子符合彭德里变换。与迄今已知的情况不同，当前的几何变换从威利斯介质开始，并进一步假设原始介质中的位移场u和变换后介质中的位移场u'保持不变（u' = u）。这打破了威利斯方程中描述变换后有效介质的四阶和三阶张量的微小对称性。当剪切极化源位于被结构化隐身衣包围的夹紧障碍物附近时，在特定的、共振的亚波长频率下，我们实现了一定程度的隐身。尽管存在潜在的手性弹性效应，但近似有效介质的结构化介质允许强威利斯耦合，从而减轻了威利斯介质和柯塞尔介质在实现的弹性动力学隐身中的作用。
