Miura-Ori, a celebrated origami pattern that facilitates functionality in matter, has found multiple applications in the field of mechanical metamaterials. Modifications of Miura-Ori pattern can produce curved configurations during folding, thereby enhancing its potential functionalities. Thus, a key challenge in designing generalized Miura-Ori structures is to tailor their folding patterns to achieve desired geometries. In this work, we address this inverse-design problem by developing a new continuum framework for the differential geometry of generalized Miura-Ori. By assuming that the perturbation to the classical Miura-Ori is slowly varying in space, we derive analytical relations between geometrical properties and the perturbation field. These relationships are shown to be invertible, allowing us to design complex curved geometries. Our framework enables porting knowledge, methods and tools from continuum theories of matter and differential geometry to the field of origami metamaterials.

中文翻译：

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折纸结构逆向设计的连续体几何方法


Miura-Ori 是一种著名的折纸图案，可促进物质的功能，在机械超材料领域已有多种应用。Miura-Ori 图案的修改可以在折叠过程中产生弯曲的形状，从而增强其潜在的功能。因此，设计广义 Miura-Ori 结构的一个关键挑战是定制其折叠模式以实现所需的几何形状。在这项工作中，我们通过为广义 Miura-Ori 的微分几何开发一个新的连续体框架来解决这个逆向设计问题。通过假设对经典 Miura-Ori 的扰动在空间中缓慢变化，我们推导出几何性质和扰动场之间的解析关系。这些关系被证明是可逆的，使我们能够设计复杂的弯曲几何图形。我们的框架能够将知识、方法和工具从物质的连续体理论和微分几何移植到折纸超材料领域。