Robust folding of elastic origami
Robust folding of elastic origami
复制标题
弹性折纸的坚固折叠
DOI：
10.1039/d2sm00369d
复制
发表时间：
2022
期刊：
影响因子：
3.4
通讯作者：
Santangelo, Christian D.
中科院分区：
文献类型：
--
作者：
Lee-Trimble, M. E.;Kang, Ji-Hwan;Hayward, Ryan C.;Santangelo, Christian D.
自折叠折纸是一种将平面设计为折叠成有针对性的三维形状的结构，具有许多潜在的工程应用。尽管近年来人们致力于设计能够实现各种目标形状的折叠图案，但最近的工作也清楚地表明，许多折纸结构表现出多条折叠路径，随着折叠结构变得复杂，几何折叠路径的数量激增。这些途径之间的竞争可能导致为一个形状编程的结构，但折叠不正确。为了解开导致错误折叠的特征，我们引入了一个自折叠折纸模型，该模型解释了折纸面的有限拉伸刚性，并允许计算导致错误折叠的能量景观。我们发现，除了折纸的几何特征外，接近平坦的折纸构型的有限弹性还通过一系列鞍结分叉来调节潜在错折态的扩散。我们将我们的模型应用于最常见的折纸图案之一，对称的“鸟脚”，即有四个折叠的单个顶点。我们发现，即使程序折叠角度中的一个小错误也会导致刚性折纸的亚稳定，但弹性允许人们调整对错误折叠的弹性。在一个更复杂的设计中，“兰德利特扑翼鸟”，它有数千个潜在的竞争状态，我们进一步证明，实际观察到的极小值的数量强烈地取决于结构的弹性。总体而言，我们表明，弹性折纸具有较硬的折叠和较少弯曲的表面更好地自我折叠。
Self-folding origami, structures that are engineered flat to fold into targeted, three-dimensional shapes, have many potential engineering applications. Though significant effort in recent years has been devoted to designing fold patterns that can achieve a variety of target shapes, recent work has also made clear that many origami structures exhibit multiple folding pathways, with a proliferation of geometric folding pathways as the origami structure becomes complex. The competition between these pathways can lead to structures that are programmed for one shape, yet fold incorrectly. To disentangle the features that lead to misfolding, we introduce a model of self-folding origami that accounts for the finite stretching rigidity of the origami faces and allows the computation of energy landscapes that lead to misfolding. We find that, in addition to the geometrical features of the origami, the finite elasticity of the nearly-flat origami configurations regulates the proliferation of potential misfolded states through a series of saddle-node bifurcations. We apply our model to one of the most common origami motifs, the symmetric “bird's foot,” a single vertex with four folds. We show that though even a small error in programmed fold angles induces metastability in rigid origami, elasticity allows one to tune resilience to misfolding. In a more complex design, the “Randlett flapping bird,” which has thousands of potential competing states, we further show that the number of actual observed minima is strongly determined by the structure's elasticity. In general, we show that elastic origami with both stiffer folds and less bendable faces self-folds better.