Phase diagram and mechanics of snap-folding of ring origami by twisting. (1st July 2022) - Sun, Xiaohao; Wu, Shuai; Dai, Jize; Leanza, Sophie; Yue, Liang; Yu, Luxia; Jin, Yi; Jerry Qi, H.; Zhao, Ruike Renee
Highlights: Snap-folding mechanics of differently shaped ring structures (circular, elliptical, rounded rectangular, and rounded triangular rings) under twisting loads is studied. Various folding modes in terms of foldability, stability and snapping type are identified. Phase diagrams of the folding modes with respect to geometric parameters are constructed. Diagrams of the areal packing ratios are constructed using the reduced planar rod model. The results provide mechanics insights into the ring snap-folding and can guide the design of ring-origami assembly. Abstract: Ring origami is a new strategy to design bistable foldable/deployable structures by assembling multiple rings with the same geometry. The successful folding of ring origami assembly leverages the snap-folding capability of single rings. It is thus important to model the snap-folding of ring-shaped structures for the rational design of ring origami with good foldability, stability and high areal packing ratio. This paper studies the folding mechanics of differently shaped rings (circular, elliptical, rounded rectangular and rounded triangular rings) under twisting loads by developing theoretical and three-dimensional finite element analysis (FEA) models. The rod model is re-formulated for different ring geometries as two-point boundary value problem systems, which are then solved through numerical continuation, allowing one to capture complex equilibrium paths with multiple fold points. The rod model, verified by FEA simulations and experiments, can accurately, quantitatively capture the snap-folding behaviors for rings of different geometries. Using the rod model, we analyze the folding modes in terms of foldability, stability and snapping type. Phase diagrams of folding modes are then constructed with respect to geometric parameters for the ring profile and cross-section for differently shaped rings. Diagrams of areal packing ratios are obtained using the reduced planar rod model. This work provides comprehensive mechanics insights into the ring folding through twisting and can guide future ring origami design.