Curved Ring Origami: Bistable Elastic Folding for Magic Pattern Reconfigurations

Ring origami has emerged as a robust strategy for designing foldable and deployable structures due to its impressive packing abilities achieved from snap-folding. In general, polygonal rings with rationally designed geometric parameters can fold into compact three-loop configurations with curved segments which result from the internal bending moment in the folded state. Inspired by the internal bending moment-induced curvature in the folded state, we explore how this curvature can be tuned by introducing initial natural curvature to the segments of the polygonal rings in their deployed stress-free state, and study how this initial curvature affects the folded configurations of the rings. Taking a clue from straight-segmented polygonal rings that fold into overlapping curved loops, we find that this behavior can be reversed by introducing curvature into the ring segments in the stress-free initial state such that the rings fold into a looped straight-line configuration with “zero” area. This strategy realizes extreme packing of the rings. In this work, by a combination of experimental observation, finite element analysis, and theoretical modeling, we systematically study the effect of segment curvature on folding behaviors, folded configurations, and packing abilities of curved ring origami with different geometries. It is anticipated that curved ring origami can open a new avenue for the design of foldable and deployable structures with simple folded configurations and high packing efficiency.