Materials Department, University of California, Santa Barbara, California 93106-5050, USA.
Department of Mechanical Engineering, University of California, Santa Barbara, California 93106-5050, USA.
Nature. 2017 Mar 23;543(7646):533-537. doi: 10.1038/nature21075. Epub 2017 Feb 20.
A wide variety of high-performance applications 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, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. 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, 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. 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, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple design can be manufactured using origami-like sheet folding and bonding methods.
各种各样的高性能应用都需要在承受很大应力的情况下保持形状控制的材料，并且密度要最小化。受生物启发的六边形和正方形蜂窝结构以及基于由网或桁架组成的重复单元的晶格材料，当由高弹性刚度和低密度的材料制成时，代表了当今可用的最轻、最硬和最强的材料之一。3D 打印和自动化装配的最新进展使得能够以低成本（且不断降低的成本）制造如此复杂的材料几何形状。这些机械超材料的性能是其细观几何形状以及其组成部分的函数，导致了在固体材料中无法获得的性能组合；然而，尚未确定实现各向同性弹性和应变储能的理论上限（Hashin-Shtrikman 上限）的材料几何形状。在这里，我们评估了在代表性的材料几何形状选择下负载下应变能的分布方式，以确定与高弹性性能相关的形态特征。我们使用有限元模型，辅以分析方法和启发式优化方案，确定了一种实现各向同性弹性刚度的 Hashin-Shtrikman 上限的材料几何形状。以前的工作集中在桁架网络和各向异性蜂窝上，这两者都无法达到这一理论极限。我们发现需要刚性但分布良好的板状网络来在相邻构件之间有效地传递负载。由此产生的低密度机械超材料具有许多有利的特性：它们的细观几何形状可以促进具有高能量吸收的大压缩应变、光学带隙和机械可调谐声学带隙、高隔热、浮力以及流体储存和运输。我们相对简单的设计可以使用类似折纸的片状折叠和粘结方法制造。
