Some results on the Guest–Hutchinson modes and periodic mechanisms of the Kagome lattice metamaterial
Some results on the Guest–Hutchinson modes and periodic mechanisms of the Kagome lattice metamaterial
复制标题
Kagome晶格超材料Guest-Hutchinson模式和周期机制的一些结果
DOI：
10.1016/j.jmps.2023.105311
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发表时间：
2023
影响因子：
5.3
通讯作者：
Kohn, Robert V.
中科院分区：
文献类型：
--
作者：
Li, Xuenan;Kohn, Robert V.
晶格材料是一种有趣的力学超材料，其力学性能往往与机制的存在有关。周期机制的存在可以通过Guest-Hutchinson（GH）模式的存在来表示，因为GH模式有时是周期机制的无穷小版本。然而，并不是每个GH模式都来自周期性机制。本文件的重点是：（1）阐明了GH模与周期机制的关系;（2）回答了哪些GH模来自周期机制的问题。我们主要集中在一个特殊的晶格系统，Kagome格。我们的结果包括明确的公式，所有的两个周期机制的Kagome晶格，和一个必要条件的GH模式来从一个周期机制一般。我们把这个必要条件应用到双周期GH模中，也应用到Fleck和哈钦森在Kagome晶格上用Bloch型边界条件发现的一些特殊的GH模中。
Lattice materials are interesting mechanical metamaterials, and their mechanical properties are often related to the presence of mechanisms. The existence of periodic mechanisms can be indicated by the presence of Guest–Hutchinson (GH) modes, since GH modes are sometimes infinitesimal versions of periodic mechanisms. However, not every GH mode comes from a periodic mechanism. This paper focuses on: (1) clarifying the relationship between GH modes and periodic mechanisms; and (2) answering the question: which GH modes come from periodic mechanisms? We focus primarily on a special lattice system, the Kagome lattice. Our results include explicit formulas for all two-periodic mechanisms of the Kagome lattice, and a necessary condition for a GH mode to come from a periodic mechanism in general. We apply our necessary condition to the two-periodic GH modes, and also to some special GH modes found by Fleck and Hutchinson using Bloch-type boundary conditions on the unit cell of the Kagome lattice.