Morphology transitions of twisted ribbons: Dependence on tension and geometry

Slender ribbons can be stretched, bent, and twisted, exhibiting a range of complex morphologies. We study the morphology transitions of a ribbon subjected to tension and torsion by combining experiment and theory. A unified phase diagram as a function of torque and aspect ratio is constructed by comparing the microscopic and macroscopic buckling. Two distinct types of shape evolutions are identified. For the twist of a wide ribbon, the shape transforms from a helicoid through a crease to a cylinder. However, for a narrow ribbon under torsion, no crease occurs. The mechanical behavior of the stretched and twisted ribbon is described based on an energy method. It is found that the succession of transformations for the morphologies strongly depends on the aspect ratio and tension. This study sheds light on understanding the morphological complexity of a constrained slender structure.