Buckling of an ultrathin shell on a flat liquid surface

Wrinkles are ubiquitous in biological materials such as flower petals and skin, and in everyday objects like window curtains or a rolled-up shirt sleeve. Recently a far-from-threshold approach, in which wrinkles completely relax compressive stresses, has described wrinkle patterns in a variety of settings. However, the extension of this framework to a broader class of problems, including intrinsically curved films or situations with biaxial compression, remains open. We manufacture ultrathin (30 to 800 nm) polystyrene sheets on spherically-curved substrates, varying the sheet thickness, width, and curvature, and transfer the films to a flat water bath. Above a threshold curvature, we observe a circular wrinkled core with a disordered pattern of wrinkles that is characteristic of biaxial compression. At higher curvatures the sheets fold. Our measurements of the onset of wrinkles and the size of the wrinkled core are in excellent agreement with our far-from-threshold calculations with no free parameters. Although the core size is governed by the curvature of the film, the wrinkle wavelength and folding threshold are surprisingly well described by simple one-dimensional results for flat films.