Stanford
Zhao Lab

Ring Origami

Ring origami uses a snap-folding mechanism triggered by the buckling instability of rods under external loads that can induce out-of-plane deformation (e.g., bending and twisting).  It is demonstrated that the snap-through instability leads to a self-guided folding behavior while showing a high packing ratio for rings with different geometries.

Tutorial video that shows the fabrication of a curved-sided hexagram ring with four equilibrium states

Multiple equilibrium states of a curved-sided hexagram: Part I-Stability of states, Journal of the Mechanics and Physics of Solids (2023)

The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Stability limits are established in this Part I

Details
Multiple equilibrium states of a curved-sided hexagram: Part II-Transitions between states, Journal of the Mechanics and Physics of Solids (2023)

Part II presents numerical simulations of transitions using both rod theory and a three-dimensional finite element formulation

Details
On the elastic stability of folded rings in circular and straight states, European Journal of Mechanics-A/Solids (2023)

Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states are investigated analytically

Details
Curved Ring Origami: Bistable Elastic Folding for Magic Pattern Reconfigurations, Journal of Applied Mechanics (2023)

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

Details
Easy snap-folding of hexagonal ring origami by geometric modifications, Journal of the Mechanics and Physics of Solids (2023)

Here, we propose strategies to facilitate easy snap-folding of the hexagonal ring by a simple point load or localized twist or squeeze

Details
Hexagonal Ring Origami Assemblies: Foldable Functional Structures with Extreme Packing, Journal of Applied Mechanics (2022)

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

Details
Hexagonal ring origami—Snap-folding with large packing ratio, Extreme Mechanics Letters (2022)

In this work, we use finite element analysis to systematically investigate how geometric parameters, loading locations, and loading methods affect the foldability and stability of hexagonal rings

Details
Ring Origami: Snap‐Folding of Rings with Different Geometries, Advanced Intelligent Systems (2021)

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

Details