基于扭曲Kagome点阵结构的一模材料设计  

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

作　　者：刘晓宁 万力臣 Xiaoning Liu;Lichen Wan(Key Laboratory of Dynamics and Control of Flight Vehicle,School of Aerospace Engineering,Beijing Institute of Technology,Beijing,100081)

机构地区：[1]北京理工大学宇航学院飞行器动力学与控制教育部重点实验室,北京100081

出　　处：《固体力学学报》2022年第5期564-576,共13页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11972080,11972083)资助。

摘　　要：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.论文对扭曲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.Metamaterials with zero-energy mode are a kind of elastic materials 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 materials. 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 materials with zero-energy modes remain almost untouched. In this study, we presented a comprehensive development for the 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, and thus can correctly predict the rank-deficient effective elastic tensor. Further, the relations between the microscopic self-stress and mechanism states as well as the macroscopic hard and soft modes were clarified. In particular, for distorted Kagome lattices, we were able to analytically express the soft mode by irreducible geometric parameters, with the rest parameters including the bar stiffness 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 was 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 the 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 a uni-mode material may possess open shape, which is not found in ordinary orthotropic materials, and can be utilized in the wideband negative refraction of elastic wave beam. The w

关 键 词：点阵材料 弹性超材料 一模材料 有效性质 微结构设计 

分 类 号：TB34[一般工业技术—材料科学与工程]