Berry M, Lee-Trimble M E, Santangelo C D
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Department of Physics, Syracuse University, Syracuse, New York 13244, USA and Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev E. 2020 Apr;101(4-1):043003. doi: 10.1103/PhysRevE.101.043003.
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.
折纸结构已被提议作为一种从微观到宏观尺度创建三维结构的方法，以及制造机械超材料的一种手段。此类结构的设计需要对折纸折叠图案的运动学有深入理解。在这里，我们研究非欧几里得折纸的构型，即高斯曲率集中在顶点的折叠结构，适用于任意折纸折叠图案。此类结构的运动学关键取决于高斯曲率的符号。作为我们一般结果的一个应用，我们表明具有正高斯曲率的不相交、有向顶点的构型空间分解为不相连的子空间；在不撕裂折纸的情况下，它们之间不存在路径。相比之下，负高斯曲率顶点的构型空间保持连通。这提供了一种新的、且仅部分被探索的机制，通过该机制可以控制折纸结构的力学和折叠。
