A wrinkled cylindrical shell as a tunable locking material*

Consider the final step to place a fitted bed sheet on a mattress. At first it is easy to pull the crumpled corner outward, until the fabric becomes taut and "locks" into place. Here, we use a thin sheet to form a system where the locking behavior is tunable: a cylindrical shell that is subjected to axial compression and twist. After an initial compression, the crumpled shell can be twisted with little resistance until it reaches a "locking angle", which coincides with the appearance of an ordered wrinkle pattern. We construct a simple geometric model to predict the locking angle as a function of the axial compression, which we cast as a phase boundary between relaxed and stretched states. We then conduct force-controlled experiments, where we apply a small tension to the shell while twisting it with a rheometer. These experiments allow us to measure the locking angle and the orientation of wrinkles, in excellent agreement with our model. Our results establish a route to a tunable locking material—a system that can be freely deformed within some interval, whose endpoints can be changed continuously over a wide range.