Mechanical metamaterials present a promising platform for seemingly impossible mechanics. They often require incompatibility of their elementary building blocks, yet a comprehensive understanding of its role remains elusive. Relying on an analogy to ferromagnetic and antiferromagnetic binary spin interactions, we present a universal approach to identify and analyze topological mechanical defects for arbitrary building blocks. We underline differences between two- and three-dimensional metamaterials, and show how topological defects can steer stresses and strains in a controlled and non-trivial manner and can inspire the design of materials with hitherto unknown complex mechanical response.

中文翻译：

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旋转超材料：机械不兼容作为磁挫败

机械超材料为看似不可能的力学提供了一个有前途的平台。它们通常需要它们的基本构建块不兼容，但对其作用的全面理解仍然难以捉摸。依靠对铁磁和反铁磁二元自旋相互作用的类比，我们提出了一种通用方法来识别和分析任意构建块的拓扑机械缺陷。我们强调了二维和三维超材料之间的差异，并展示了拓扑缺陷如何以可控和非平凡的方式引导应力和应变，并可以激发具有迄今为止未知的复杂机械响应的材料设计。