Ordered buckling structures in a twisted crimped tube

When a ribbon or tube is twisted far enough it forms buckles and wrinkles. Its new geometry can be strikingly ordered, or hopelessly disordered. Here we study this process in a tube with hybrid boundary conditions: one end a cylinder, and the other end crimped flat like a ribbon, so that the sample resembles a toothpaste tube. The resulting irregular structures and mechanical responses can be dramatically different from those of a ribbon. However, when we form two creases in the tube prior to twisting, we obtain an ordered structure composed of repeating triangular facets oriented at varying angles, and a more elastic torque response, reminiscent of the creased helicoid structure of a twisted ribbon. We measure how the torque and structural evolution depend on parameters such as material thickness and the twist angle. When only part of the tube is pre-creased, the ordered structures are confined to this segment. Surprisingly, in some tubes made from thicker sheets, an ordered structure forms without pre-creasing. This study provides insights into controlling the buckling of thin shells, offering a potential pathway for designing ordered structures in soft materials.