Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness
Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness
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DOI：
10.1038/nature21075
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发表时间：
2017-03-23
期刊：
影响因子：
64.8
通讯作者：
Mcmeeking, R. M.
中科院分区：
文献类型：
--
作者：
Berger, J. B.;Wadley, H. N. G.;Mcmeeking, R. M.
各种各样的高性能应用（1）需要在相当大的应力下保持形状控制的材料，并且具有最小的密度。生物启发的六边形和正方形蜂窝结构和基于由网或桁架组成的重复单元格的晶格材料（2），当由高弹性刚度和低密度的材料制成时（3），代表了当今可用的一些最轻、最硬和最强的材料（4）。3D打印和自动化组装的最新进展使这种复杂的材料几何形状能够以低成本（并且不断下降）制造。这些机械超材料具有的特性是其介观几何形状及其成分的函数（3，5 -12），导致固体材料中无法获得的特性组合;然而，实现各向同性弹性和应变能存储的理论上限（Hashin-Shtrikman上限）的材料几何形状尚未确定。在这里，我们评估的方式，应变能分布在负载下的一个代表性的选择材料的几何形状，以确定与高弹性性能的形态特征。使用有限元模型，分析方法和启发式优化方案的支持下，我们确定了材料的几何形状，实现各向同性弹性刚度的Hashin-Shtrikman上界。以前的工作主要集中在桁架网络和各向异性蜂窝上，这两种都不能达到这个理论极限（13）。我们发现，刚性，但分布均匀的板网络需要有效地转移相邻成员之间的负载。所得到的低密度机械超材料具有许多有利的特性：它们的中尺度几何形状可以促进具有高能量吸收（2，14，15）的大的压碎应变、光学带隙（16-19）和机械可调的声学带隙（20）、高的热绝缘（21）、浮力以及流体存储和运输。我们的相对简单的设计可以使用折纸样的片材折叠（22）和粘合方法来制造。
A wide variety of high-performance applications(1) require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses(2), when made from materials of high elastic stiffness and low density(3), represent some of the lightest, stiffest and strongest materials available today(4). Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents(3,5-12), leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin-Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin-Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit(13). We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption(2,14,15), optical bandgaps(16-19) and mechanically tunable acoustic bandgaps(20), high thermal insulation(21), buoyancy, and fluid storage and transport. Our relatively simple design can be manufactured using origami-like sheet folding(22) and bonding methods.