Multiscale Modeling &Simulation, Volume 19, Issue 2, Page 633-664, January 2021.
We make precise some results on the cloaking of displacement fields in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosserat and Willis frameworks are shown to be equivalent to certain high-contrast small defect problems for the usual Navier equations. We discuss near-cloaking for elasticity systems via a regularized transform and perform numerical experiments to illustrate our near-cloaking results. We also study the sharpness of the estimates from [H. Ammari, H. Kang, K. Kim, and H. Lee, J. Differential Equations, 254 (2013), pp. 4446--4464], wherein the convergence of the solutions to the transmission problems is investigated, when the Lamé parameters in the inclusion tend to extreme values. Both soft and hard inclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose an approximate isotropic cloak algorithm for a symmetrized Cosserat cloak.

中文翻译：

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线弹性的近隐形

多尺度建模与仿真，第 19 卷，第 2 期，第 633-664 页，2021 年 1 月。
我们对线性弹性中位移场的掩蔽做出了精确的一些结果。本着变换介质理论的精神，Cosserat 和 Willis 框架中的变换控制方程被证明等效于通常 Navier 方程的某些高对比度小缺陷问题。我们通过正则化变换讨论弹性系统的近隐形，并进行数值实验来说明我们的近隐形结果。我们还研究了 [H. Ammari, H. Kang, K. Kim 和 H. Lee, J. Differential Equations, 254 (2013), pp. 4446--4464]，其中研究了传输问题解的收敛性，当 Lamé 参数在夹杂中趋于极端值。研究了软夹杂物和硬夹杂物的限制，我们还涉及有限频率的情况。最后，我们为对称的 Cosserat 斗篷提出了一种近似的各向同性斗篷算法。