Anomalous strain energy transformation pathways in mechanical metamaterials
Anomalous strain energy transformation pathways in mechanical metamaterials
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DOI：
10.1098/rspa.2019.0041
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发表时间：
2019-06-01
影响因子：
3.5
通讯作者：
Klein, John T.
中科院分区：
文献类型：
--
作者：
Karpov, Eduard G.;Danso, Larry A.;Klein, John T.
本讨论从力学版本的Parseval能量定理开始，适用于任何具有周期性内部结构的离散晶格材料：微桁架，网格，框架，折纸或镶嵌。它提供了一个简单的应变能体积/通常和频谱分布在倒易空间之间的关系。谱能量分布直接导致晶格变形的谱熵（香农型），其与材料坐标的方差表示关于材料内部中的表面载荷的信息的减少。谱熵也是超材料对表面和主体载荷的机械响应的复杂性的基本度量。考虑变换的能量体积和光谱分布的材料坐标指向远离表面负载，几个有趣的异常，即使是简单的晶格材料相比，连续材料。这些异常包括表面罗利波（正弦压力模式）的选择性过滤，圣维南效应反演所示的能量谱分布轮廓，发生“隐藏口袋”的低变形，和重定向的应变能最大值远离轴的集中表面负载。后一种现象对于机械超材料的冲击保护应用可能是重要的。
This discussion starts with a mechanics version of Parseval's energy theorem applicable to any discrete lattice material with periodic internal structure: a microtruss, grid, frame, origami or tessellation. It provides a simple relationship between the strain energy volumetric/usual and spectral distributions in the reciprocal space. The spectral energy distribution leads directly to a spectral entropy of lattice deformation (Shannon's type), whose variance with a material coordinate represents the decrease of information about surface loads in the material interior. Spectral entropy is also a basic measure of complexity of mechanical responses of metamaterials to surface and body loads. Considering transformation of the energy volumetric and spectral distributions with a material coordinate pointed away from a surface load, several interesting anomalies are seen even for simple lattice materials, when compared to continuum materials. These anomalies include selective filtering of surface Raleigh waves (sinusoidal pressure patterns), Saint-Venant effect inversion illustrated by energy spectral distribution contours, occurrence of 'hiding pockets' of low deformation, and redirection of strain energy maximum away from axis of a concentrated surface load. The latter phenomenon can be significant for impact protection applications of mechanical metamaterials.