John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138;
Proc Natl Acad Sci U S A. 2019 Apr 23;116(17):8119-8124. doi: 10.1073/pnas.1820505116. Epub 2019 Apr 5.
Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale-invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.
具有大量多余褶皱的折纸结构能够存储能量等效的可区分的几何状态。随着多余褶皱数量的减少，系统具有更少的等效状态，最终可能变得僵硬。我们将这种从柔软到坚硬的状态的转变作为经典折纸镶嵌 Miura-ori 中折叠约束存在的函数来量化。我们表明，在完全三角化的 Miura-ori 中，通过消除四边形中的对角折叠来增加约束，会首先线性然后非线性地减少系统的自由度。在非线性区域，通过约束分配的冗余，机械协同作用开始发挥作用，自由度以标度不变的方式取决于约束密度。约束冗余作为约束密度函数的渗流转变表明，折纸结构中的多余褶皱如何以标度不变的方式存储几何信息。
