Measuring the Transition from Wrinkles to Crumples in Stamped Thin Sheets

Wrapping a basketball with a sheet of wrapping paper is a frustrating exercise. The geometries of the planar sheet and the spherical surface are incompatible, resulting in a rough, crinkled appearance. These deformations can occur in any sufficiently thin sheet confined to a surface with a different metric, such as in the use of wearable sensors or synthetic skins. Recent studies have characterized a transition from smooth “wrinkles” to sharp “crumples” in thin polymer films placed on curved liquid surfaces. Their experiments established a threshold for this transition, which depends on the boundary tension, the imposed curvature, the length of the buckled region, and the stretching modulus of the material. But, how do the parameters governing the wrinkle to crumple transition change in the absence of surface tension pulling at the boundary of the film?

We report experiments using a pair of curved glass lenses to stamp a thin sheet placed between them. We find that the wrinkle to crumple transition depends on the sheet's thickness, the sheet's diameter, and the imposed curvature; and we identify an empirical threshold from wrinkles to crumples based on these parameters. Our work expands the range of environments in which the wrinkle to crumple transition can be predicted, which will lead to a more generic description of the transition.