Twist-induced snapping in a bent elastic ribbon

Snapping a slender structure is utilized in a wide range of natural and man-made systems, 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 to design such a kinetic system is a key challenge in mechanics. Here we study a twist-driven buckling and flip dynamics of a geometrically constrained ribbon by combining experiments, 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 determined by geometry. We quantify effects of gravity and timescale dictating the flipping. Our study reveals the unique role of 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.