Ring Origami

Here, we introduce a concept of segmented rings with intrinsic multistability by programming the natural curvature of the rod segments. Guided by theoretical modeling, simulation, and experimental validation, we demonstrate that a segmented ring with a rectangular cross-section can exhibit up to six distinct planar stable states characterized by uniform bending in each segment. The segmented rings constitute what are probably the simplest elastic structural entities with multiple stable states, and they will serve to expand the application space of functional multistable structures.

s. In Part I, the classical stability criterion based on energy variation was used to study the elastic stability of the curved-sided hexagram and identify the natural curvature range for the stability of each state with circular and rectangular rod cross-sections. Here, we combine a multisegment Kirchhoff rod model, finite element simulations, and experiments to investigate the transitions between four basic equilibrium states of the curved-sided hexagram. 

The initial curvature of the rings is tuned to study how this initial curvature affects the folded configurations of the rings

Motivated by this significant packing, we utilize a combination of experiments and finite element analysis to study effective folding strategies and packing abilities of various 2D and 3D hexagonal ring assemblies

Motivated by the large area change and the self-guided deformation through snap-folding of the rings (circular, elliptical, rounded rectangular, and rounded triangular shapes), this work introduces ring origami assemblies with unprecedented packing ratios