Mechanical metamaterials, also known as architected materials, are rationally designed composites, aiming at elastic behaviors and effective mechanical properties beyond (‘meta’) those of their individual ingredients—qualitatively and/or quantitatively. Due to advances in computational science and manufacturing, this field has progressed considerably throughout the last decade. Here, we review its mathematical basis in the spirit of a tutorial, and summarize the conceptual as well as experimental state-of-the-art. This summary comprises disordered, periodic, quasi-periodic, and graded anisotropic functional architectures, in one, two, and three dimensions, covering length scales ranging from below one micrometer to tens of meters. Examples include extreme ordinary linear elastic behavior from artificial crystals, e.g. auxetics and pentamodes, ‘negative’ effective properties, behavior beyond classical linear elasticity, e.g. arising from local resonances, chirality, beyond-nearest-neighbor interactions, quasi-crystalline mechanical metamaterials, topological band gaps, cloaking based on coordinate transformations and on scattering cancelation, seismic protection, nonlinear and programmable metamaterials, as well as space-time-periodic architectures.

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机械超材料


机械超材料，也称为建筑材料，是合理设计的复合材料，旨在定性和/或定量地超越其单个成分（“元”）的弹性行为和有效机械性能。由于计算科学和制造的进步，该领域在过去十年中取得了长足的进步。在这里，我们本着教程的精神回顾其数学基础，并总结概念和实验的最新技术。该摘要包括一维、二维和三维的无序、周期性、准周期性和渐变各向异性功能架构，涵盖从一微米以下到数十米的长度尺度。例子包括人造晶体的极端普通线弹性行为，例如人造晶体。拉胀和五模态、“负”有效特性、超越经典线性弹性的行为，例如由局部共振、手性、超最近邻相互作用、准晶机械超材料、拓扑带隙、基于坐标变换和散射消除的隐身、地震防护、非线性和可编程超材料以及时空周期产生架构。