Norris Andrew N, Parnell William J
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, USA.
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
Proc Math Phys Eng Sci. 2020 Aug;476(2240):20190725. doi: 10.1098/rspa.2019.0725. Epub 2020 Aug 5.
New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core-shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, and with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed 'unphysical' materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit.
在二维弹性力学的背景下，建立了静态弹性隐身、低频弹性波散射与中性夹杂（NIs）之间的新联系。一个被圆柱壳包围的圆柱芯嵌入均匀弹性基体中。给定芯部和基体的特性，我们回答了如何选择壳材料，使得（i）它起到静态弹性隐身的作用，以及（ii）它消除入射弹性波的低频散射。结果表明，静态隐身（i）需要一个各向异性的壳，而散射减少（ii）可以用各向同性材料更简单地实现。通过将芯-壳复合圆柱视为中性弹性夹杂，得到了壳材料的隐式解。区分了两种类型的NI，其中前者等同于低频透明性以及1979年经典的克里斯滕森和洛关于面内剪切的广义自洽结果。我们对 的引入是这一结果的重要扩展，因为我们表明标准的各向异性壳可以作为完美的静态隐身衣，这与之前使用“非物理”材料的工作形成对比。低频透明性、静态隐身和NIs之间的关系为准静态极限下实现弹性隐身的材料设计者提供了选择。
