An equilibrium phase diagram for the shape of compressively strained free-hanging films is developed by total strain energy minimization. For small strain gradients {Delta}{epsilon}, the film wrinkles, while for sufficiently large {Delta}{epsilon}, a phase transition from wrinkling to bending occurs. We consider competing relaxation mechanisms for free-hanging films, which have rolled up into tube structures, and we provide an upper limit for the maximum achievable number of tube rotations.
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