2D-to-3D transformation of ring origami via snap-folding instabilities
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Here, we propose a 2D-to-3D shape transformation strategy for ring origami by introducing out-of-plane natural curvature (i.e., the stress-free curved state lies in a plane perpendicular to the planar ring) into the rod segments. Due to natural curvature-induced out-of-plane bending moments, a 2D elastic ring spontaneously snaps out-of-plane and reaches equilibrium in a 3D configuration. These snapping-induced out-of-plane shape transitions not only enable self-guided, spontaneous shape morphing, but also allow the construction of complex structures from simple geometries, making them promising for the design of functional deployable and foldable structures.