We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a homogeneous isotropic linear elastic material of prescribed shear modulus. Importantly, we find that the same combination of annuli will cloak any possible mode of imposed deformation or loading, for any randomly chosen admixture of imposed compression, pure shear and simple shear, without the need to re-design the cloak for different deformation modes. A full range of circular inclusions can be cloaked in this way, from soft to stiff. In consequence, we suggest that an inclusion of any arbitrary shape can also be cloaked, by first enveloping it in a stiff circle, then cloaking the combined structure with three annuli as described. Given that a single inclusion can be fully cloaked in this way, even at near field close to the cloaking perimeter, it also follows that multiple such neutral inclusions arranged with arbitrarily high packing fraction in a surrounding medium can also be cloaked. We confirm this by direct simulation. This indicates a possible route to fabricating composite materials with the same global mechanical response as a counterpart homogeneous material, and with uniform strain and stress fields outwith the cloaked inclusions.

中文翻译：

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简单有效的机械隐形


我们从理论上证明，通过包含三个同心环的简单斗篷，可以实现均匀周围介质中圆形夹杂物的基本完美的弹性静力学机械斗篷，每个同心环均由具有规定剪切模量的均匀各向同性线弹性材料形成。重要的是，我们发现，对于任何随机选择的外加压缩、纯剪切和简单剪切的混合，相同的环空组合将掩盖任何可能的外加变形或载荷模式，而无需针对不同的变形模式重新设计外衣。从柔软到坚硬的各种圆形内含物都可以通过这种方式隐藏。因此，我们建议任何任意形状的内含物也可以被隐藏，首先将其包围在一个刚性的圆圈中，然后如上所述用三个环形来隐藏组合结构。鉴于单个夹杂物可以通过这种方式完全隐形，即使在接近隐形周界的近场处，也可以得出结论，在周围介质中以任意高堆积分数排列的多个此类中性夹杂物也可以被隐形。我们通过直接模拟证实了这一点。这表明了一种制造复合材料的可能途径，该复合材料具有与对应的均质材料相同的整体机械响应，并且具有均匀的应变和应力场且没有隐形夹杂物。