Topological transitions in the configuration space of non-Euclidean origami
Topological transitions in the configuration space of non-Euclidean origami
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DOI：
10.1103/physreve.101.043003
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发表时间：
2020-04-23
影响因子：
2.4
通讯作者：
Santangelo, C. D.
中科院分区：
文献类型：
--
作者：
Berry, M.;Lee-Trimble, M. E.;Santangelo, C. D.
折纸结构已被提出作为一种手段，创造三维结构，从微观到宏观尺度，并作为一种手段，制造机械超材料。这种结构的设计需要对折纸折叠模式的运动学有深刻的理解。在这里，我们研究的配置非欧几里德折纸，折叠结构与高斯曲率集中在顶点上，任意折纸折叠模式。这种结构的运动学关键取决于高斯曲率的符号。作为我们的一般结果的应用，我们表明，不相交的配置空间，定向顶点与正高斯曲率分解成不连通的子空间，没有他们之间的路径没有撕裂的折纸。相反，负高斯曲率顶点的位形空间保持连通。这提供了一种新的，仅部分探索的机制，通过该机制可以控制折纸结构的力学和折叠。
Origami structures have been proposed as a means of creating three-dimensional structures from the micro- to the macroscale and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding of the kinematics of origami fold patterns. Here we study the configurations of non-Euclidean origami, folding structures with Gaussian curvature concentrated on the vertices, for arbitrary origami fold patterns. The kinematics of such structures depends crucially on the sign of the Gaussian curvature. As an application of our general results, we show that the configuration space of nonintersecting, oriented vertices with positive Gaussian curvature decomposes into disconnected subspaces; there is no pathway between them without tearing the origami. In contrast, the configuration space of negative Gaussian curvature vertices remains connected. This provides a new, and only partially explored, mechanism by which the mechanics and folding of an origami structure could be controlled.