论文标题
基于机理的超材料的二元性和剪切分析响应
Duality and Sheared Analytic Response in Mechanism-Based Metamaterials
论文作者
论文摘要
机械超材料围绕变形的零能量途径（称为一种机制）反复挑战了弹性的常规图片。但是，复杂的空间变形这些结构能够在统一机制之外支撑，在很大程度上仍未讲述。在这里，我们提出了一个统一的理论框架，表明在二维结构中的任何均匀机制的存在从根本上通过承认零能量变形的家族来改变其弹性响应。我们的形式主义揭示了这些无压力菌株之间的数学二元性，我们将其称为“剪切分析模式”和压力的支持空间特征。这些模式从批量周期性响应到evanescent表面响应进行了过渡，因为泊松的比率$ν$通过$ν= 0 $的特殊点调节。我们建议将这些异常响应属性作为可切换信号放大器和过滤器，用于机械电路和计算。
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.
