简单有效的机械隐形

Suzanne M. Fielding
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引用次数: 0

摘要

我们从理论上证明,通过由三个同心环形体组成的简单斗篷,可以实现均质周围介质中圆形内含物的基本完美的弹性静力学斗篷,每个环形体都是由规定佘模量的均质各向同性线性弹性材料形成的。重要的是,我们发现相同的环形体组合可以遮蔽任何可能的外加变形或加载模式,对于任何随机选择的外加压缩、纯剪切和简单剪切的混合物,无需为不同的变形模式重新设计遮蔽体。通过这种方法,可以对从软到硬的各种圆形夹杂物进行隐形。因此,我们建议,任何任意形状的内含物也可以进行隐形,方法是先将其包覆在一个坚硬的圆形中,然后按照所述方法用三个环形结构对组合结构进行隐形。鉴于单个包裹体可以通过这种方式完全隐形,甚至在接近隐形周边的近场也可以隐形,因此在周围介质中以任意高的堆积分数排列的多个中性包裹体也可以隐形。我们通过直接模拟证实了这一点。这为制造具有与同类均质材料相同的全局机械响应,并且在隐形夹杂物之外具有均匀应变和应力场的复合材料提供了可能的途径。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simple and effective mechanical cloaking
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.
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