Physics Department, Cornell University, Ithaca, New York 14853, USA.
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Nat Mater. 2015 Apr;14(4):389-93. doi: 10.1038/nmat4232. Epub 2015 Mar 9.
Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet's material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.
折纸不仅用于纯美学追求，还用于设计响应式和可定制的机械超材料。然而，由于确定局部运动学约束是否全局兼容的挑战，以及对折叠片材的材料性能如何影响整体力学响应的理解不完整，折纸的通用物理理解仍然难以捉摸。在这里，我们表明，传统的正方形扭结，其折痕模式具有零自由度（DOF），因此不应该可折叠，但通过访问不在折痕模式中的弯曲变形，仍然可以折叠。这些隐藏的弯曲自由度与折痕自由度通过能量间隙隔开，这导致单稳态和双稳态之间的几何驱动临界分岔。鉴于其在制造机械开关方面的潜在应用，我们使用温度响应聚合物凝胶版的正方形扭结来证明亚毫米尺度下的滞后折叠动力学。
