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 folded structure stemming from mechanical equilibrium yields angles at the vertices between sections of the central fold, producing an effective curvature. Both finite element analysis and manually made origamis show a robust empirical relation between the imprinted crease network’s dimensions and the apparent curvature. Moreover, the emerging structure exhibits various elastic deformations that induce three distinct morphogenesis types, from bent faces to complete faceting to structural buckling. 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.

我们研究了由已折叠的手风琴状折纸形成的壳体的三维平衡形状，该折纸由弹性片制成，弹性片由一系列与中央纵向折痕交叉的平行折痕装饰。出人意料的是，虽然压痕网络没有显示出测地曲率，但由于机械平衡而产生的出现的折叠结构在中心折叠部分之间的顶点处产生了角度，从而产生了有效的曲率。有限元分析和手工制作的折纸都显示出压痕网的尺寸和表观曲率之间的稳固的经验关系。此外，新出现的结构还表现出各种弹性变形，这些变形引起了三种不同的形态发生类型，从弯曲的表面到完整的刻面再到结构屈曲。我们表征了折痕网络变形的相应运动学，并确定了它们的相图。利用由折痕刚度和折痕网络变形的运动学之间的竞争引起的挫折感，我们提供了一种新颖的工具来设计受强大几何特性约束的弯曲折纸结构。