Curving Origami with Mechanical Frustration

TL;DR

This paper investigates how elastic shells formed by accordion-like origami develop effective curvature due to central fold deformation, revealing a robust relation between crease network dimensions and resulting shape, and classifying deformation types.

Contribution

It introduces a new understanding of curvature emergence in origami shells through geometric and elastic analysis, enabling design of curved origami structures with specific properties.

Findings

Effective curvature arises from central fold deformation despite flat crease network.

Identifies three distinct elastic deformation modes and their morphogenetic implications.

Provides a phase diagram linking crease network geometry to deformation types.

Abstract

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.