Twisting a thin cylindrical film: From wrinkles to kinematic constraints*

Individual candies or lozenges may be wrapped by rolling a flat film into a cylinder, and then twisting the two ends to draw the sheet shut. Here we investigate the geometry and mechanics of this process by measuring torques and forces that occur when a thin cylindrical shell is manipulated between two flat plates. In one set of experiments, we compress a cylindrical film lengthwise and then twist it. The film shows a disordered crumpled pattern until it reaches a hard kinematic constraint, at which point an ordered pattern of wrinkles emerges and the measured torque rises rapidly. We develop a theoretical model of this process by modeling the film as an inextensible fabric that is free to compress in one direction via the formation of small-scale wrinkles. This model allows us to predict the rotation angle where the system becomes stiff, as well as the non-trivial orientation of the wrinkles. We map out these results in a phase diagram that delineates a region that may be accessed at low energetic cost, and an inaccessible region where there is macroscopic stretching. Ordered wrinkle patterns develop at the boundary between these regions, and we trace this boundary in experiments by applying a small tension force while gradually twisting the cylinder.