Twist-induced snapping in a bent elastic ribbon

Snapping of a slender structure is utilized in a wide range of natural and man-made systems, mostly to achieve rapid movement without relying on muscle-like elements. Although several mechanisms for elastic energy storage and rapid release have been studied in detail, a general understanding of the approach to design such a kinetic system is a key challenge in mechanics. Here we study a twist-driven buckling and fast flip dynamics of a geometrically constraint ribbon by combining experiments, numerical simulations, and analytical theory. We identify two distinct types of shape transitions; a narrow ribbon snaps, whereas a wide ribbon forms a pair of localized helices. We construct a phase diagram and explain the origin of the boundary, which is determined only by geometry. We quantify effects of gravity and clarify time scale dictating the rapid flipping. Our study reveals the unique role of geometric twist-bend coupling on the fast dynamics of a thin constrained structure, which has implications for a wide range of biophysical and applied physical problems.