Origami structures demonstrate great theoretical potential for creating metamaterials with exotic properties. However, there is a lack of understanding of how imperfections influence the mechanical behaviour of origami-based metamaterials, which, in practice, are inevitable. For conventional materials, imperfection plays a profound role in shaping their behaviour. Thus, this paper investigates the influence of small random geometric imperfections on the nonlinear compressive response of the representative Miura-ori, which serves as the basic pattern for many metamaterial designs. Experiments and numerical simulations are used to demonstrate quantitatively how geometric imperfections hinder the foldability of the Miura-ori, but on the other hand, increase its compressive stiffness. This leads to the discovery that the residual of an origami foldability constraint, given by the Kawasaki theorem, correlates with the increase of stiffness of imperfect origami-based metamaterials. This observation might be generalizable to other flat-foldable patterns, in which we address deviations from the zero residual of the perfect pattern; and to non-flat-foldable patterns, in which we would address deviations from a finite residual.

中文翻译：

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基于折纸的超材料中小随机缺陷的重大影响

折纸结构展示了创造具有奇异特性的超材料的巨大理论潜力。然而，人们对缺陷如何影响基于折纸的超材料的机械行为缺乏了解，这在实践中是不可避免的。对于传统材料，缺陷在塑造其行为方面起着深远的作用。因此，本文研究了小的随机几何缺陷对代表性 Miura-ori 非线性压缩响应的影响，这是许多超材料设计的基本模式。实验和数值模拟用于定量证明几何缺陷如何阻碍 Miura-ori 的可折叠性，但另一方面，会增加其压缩刚度。这导致发现由川崎定理给出的折纸可折叠性约束的残差与基于折纸的不完美超材料的刚度增加相关。这一观察结果可能适用于其他可折叠的模式，在这些模式中，我们解决了与完美模式的零残差的偏差；以及非平面可折叠模式，我们将解决与有限残差的偏差。