论文标题
微晶体弹性：零模式和拓扑极化的连续方法
Microtwist elasticity: A continuum approach to zero modes and topological polarization in Kagome lattices
论文作者
论文摘要
Kane和Lubensky（2014，Nat。Phys。10，39-45）发现的拓扑两极化等静态晶格对许多基于桁架的材料和超材料进行建模的标准有效培养基理论提出了质疑。事实上，这些表现出奇偶校验（P）的零模式的不对称分布，这些模式诱导P-空气弹性行为，这两者都无法在Cauchy弹性中复制。在这里，我们提出了一种新的有效培养基理论，受洗的“微翼弹性”，能够在宏观尺度上呈现极化效应。该理论对于在两极分化的相变的边缘上的桁架有效，在这种情况下，它们必然表现出比其尺寸更多的周期性零模式。通过将每个周期性零模式映射到宏观的自由度，微翼主义理论最终成为运动学上丰富的理论。微晶体弹性是由于领先的二尺度渐近学及其组成型和平衡方程而构建的，该方程是针对相当通用的等静态桁架的：kagome晶格。各种数值和分析计算，零模式的形状和分布，色散图和极化效应的分布，系统地显示了提出的有效培养基理论的质量。最值得注意的是，该理论能够生成凯恩和卢本斯基的拓扑极化向量的连续版本。
The topologically polarized isostatic lattices discovered by Kane and Lubensky (2014, Nat. Phys. 10, 39-45) challenged the standard effective medium theories used in the modeling of many truss-based materials and metamaterials. As a matter of fact, these exhibit Parity (P) asymmetric distributions of zero modes that induce a P-asymmetric elastic behavior, both of which cannot be reproduced within Cauchy elasticity. Here, we propose a new effective medium theory baptized "microtwist elasticity" capable of rendering polarization effects on a macroscopic scale. The theory is valid for trusses on the brink of a polarized-unpolarized phase transition in which case they necessarily exhibit more periodic zero modes than they have dimensions. By mapping each periodic zero mode to a macroscopic degree of freedom, the microtwist theory ends up being a kinematically enriched theory. Microtwist elasticity is constructed thanks to leading order two-scale asymptotics and its constitutive and balance equations are derived for a fairly generic isostatic truss: the Kagome lattice. Various numerical and analytical calculations, of the shape and distribution of zero modes, of dispersion diagrams and of polarization effects, systematically show the quality of the proposed effective medium theory. Most notably, the theory is capable of producing a continuum version of Kane and Lubensky's topological polarization vector.
