Simulations of buckling and crumpling in twisted ribbons

A twisted ribbon exhibits at least five deformation phases, with transitions facilitated by tuning the tension applied or twist angle. When driven from one of these self-avoiding phases into a disordered regime of self-contact, the ribbon develops ridges as it folds or crumples. Here, we develop a computational model of this complex, dynamic process, which reproduces the transitions seen in experimental tests. Our simulations illuminate the details of folding and crumpling transitions induced via twisting; allow careful analysis of the ribbon's topography and curvature; and potentially reveal a state variable by which the disordered system may be quantified.