弯曲折纸与机械挫折
Curving Origami with Mechanical Frustration
摘要：
我们研究的三维平衡形状的部署手风琴般的折纸，由一系列的平行折痕交叉的中央纵向折痕装饰的弹性片材形成的外壳。令人惊讶的是，虽然压印折痕网络没有表现出测地线曲率，但新兴结构的特征在于由变形的中心折叠产生的有效曲率。此外，有限元分析和手工制作的聚酯薄膜折纸都显示出压印折痕网络的尺寸和表观曲率之间的稳健经验关系。这种几何关系的详细检查表明存在三种典型的弹性形变，这反过来又导致三种不同类型的形态发生。我们描述了相应的折痕网络变形的运动学，并确定其相图。利用折痕刚度和折痕网络变形的运动学之间的竞争所造成的挫折，我们提供了一种新的工具，用于设计弯曲的折纸结构的强几何属性的约束。
英文摘要：
We study the three-dimensional equilibrium shape of a shell formed by a deployed accordion-like origami, made from an elastic sheet decorated by a series of parallel creases crossed by a central longitudinal crease. Surprisingly, while the imprinted crease network does not exhibit a geodesic curvature, the emergent structure is characterized by an effective curvature produced by the deformed central fold. Moreover, both finite element analysis and manually made mylar origamis show a robust empirical relation between the imprinted crease network's dimensions and the apparent curvature. A detailed examination of this geometrical relation shows the existence of three typical elastic deformations, which in turn induce three distinct types of morphogenesis. We characterize the corresponding kinematics of crease network deformations and determine their phase diagram. Taking advantage of the frustration caused by the competition between crease stiffness and kinematics of crease network deformations, we provide a novel tool for designing curved origami structures constrained by strong geometrical properties.
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