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 precreased, the ordered structures are confined to this segment. Surprisingly, in some tubes made from thicker sheets, an ordered structure forms without precreasing. This study provides insights into controlling the buckling of thin shells, offering a potential pathway for designing ordered structures in soft materials.