基于扭曲Kagome点阵结构的一模材料设计

零能模式超材料指弹性矩阵的特征值中有若干为零的弹性材料，根据零特征值的个数可将其分类为一模至五模材料。当前，针对五模材料已有较深入研究，并在水声和弹性波调控方面获得重要应用，而对其他类型零能模式材料的研究尚未展开。本文对扭曲Kagome周期桁架这样一类欠约束点阵材料的有效弹性性质进行了研究，结果表明通过调节点阵材料的微观几何构型和杆件刚度，该类结构能够涵盖一系列一模材料谱系。针对给定一模弹性张量，发展了软-硬模式分离的微结构逆向优化设计策略。通过特定一模材料中的波传播现象对有效性质预测和微结构设计进行了数值验证。

Design of Uni-mode Metamaterial Based on Distorted Periodic Kagome Truss Lattices

Metamaterials with zero-energy mode are a kind of elastic material that some eigenvalues of the elastic matrix are zero. By counting the number of zero eigenvalues, they are classified as from uni-mode to penta-mode material. To date, only penta-mode materials have been studied in depth and found important applications in manipulation of underwater acoustic wave and elastic wave, while other types of material with zero-energy modes remain almost untouched. In this study, we present a comprehensive development for design of two-dimensional uni-mode material based on periodic distorted Kagome truss lattices. By using the Cauchy-Born hypothesis and matrix formulation of truss systems, we developed a homogenization method for general lattices which are under-constrained. Under the macroscopic strain field, the method can take care of non-affine relaxation due to the microscopic mechanism, thus can correctly predict the rank deficient effective elastic tensor. Further, the relation between the microscopic self-stress and mechanism states as well as the macroscopic hard and soft modes is clarified. In particular, for distorted Kagome lattices, we are able to analytically express the soft mode by irreducible geometric parameters, while the rest parameters including the bar stiffnesses are responsible only for hard modes. To match a given elastic tensor, we proposed a two-level design scheme to seek microstructural parameters with high efficiency and accuracy. It is revealed that the distorted Kagome lattice is able to realize a wide spectrum of uni-mode materials via tuning its configuration. Finally, the developed method was verified in conjunction with unusual wave behaviors found in uni-mode materials, and excellent agreement was achieved between the theoretical and numerical predictions. We found that the slowness curve of an uni-mode material may possess opened shape, which is not found in ordinary orthotropic materials, and can be utilized in wideband negative refraction of elastic wave beam. The work may initiate design of more general metamaterials with zero-energy mode, and may inspire further explorations on applications other than those of penta-mode material.