基于机制的异向介质中的对偶性和剪切解析响应
Duality and Sheared Analytic Response in Mechanism-Based Metamaterials
摘要：
围绕零能量变形路径设计的机械超材料，被称为机制，一再挑战传统的弹性图像。然而，复杂的空间变形，这些结构能够支持超越统一的机制仍然在很大程度上是未知的。在这里，我们提出了一个统一的理论框架，表明在一个二维结构中的任何统一的机制的存在下，从根本上改变其弹性响应，承认一个家庭的非均匀的零能量变形。我们的形式主义揭示了这些无应力应变之间的数学对偶性，我们称之为“剪切分析模式”和支持的空间分布的应力。这些模式经历了从体周期性响应到倏逝表面响应的转变，因为该机制的泊松比$ν$通过$ν=0$处的例外点进行调谐。我们建议这些不寻常的响应特性作为可切换的信号放大器和滤波器用于机械电路和计算的第一个应用程序。
英文摘要：
Mechanical metamaterials designed around a zero-energy pathway of deformation, known as a mechanism, have repeatedly challenged the conventional picture of elasticity. However, the complex spatial deformations these structures are able to support beyond the uniform mechanism remain largely uncharted. Here we present a unified theoretical framework, showing that the presence of any uniform mechanism in a two-dimensional structure fundamentally changes its elastic response by admitting a family of non-uniform zero-energy deformations. Our formalism reveals a mathematical duality between these stress-free strains, which we term "sheared analytic modes" and the supported spatial profiles of stress. These modes undergo a transition from bulk periodic response to evanescent surface response as the Poisson's ratio $ν$ of the mechanism is tuned through an exceptional point at $ν=0$. We suggest a first application of these unusual response properties as a switchable signal amplifier and filter for use in mechanical circuitry and computation.
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