A geometric theory of wrinkling for confined shells: Part 1

The problem of joining a planar sheet to a surface with a different metric is a familiar frustration. Flat bandages don’t stick as well to curved knuckles or elbows, and maps of the earth exaggerate areas near the poles. We study the deformations of ultrathin (∼100 nm) elastic shells, which we manufacture on spherically-curved substrates and then transfer to a flat water bath. The sheets respond by forming distinct domains filled by smooth parallel wrinkles or by disordered buckled patterns. We show that the selection of these domains and the orientation of wrinkles within them depends sensitively on the shape of the boundary of the film. Remarkably, these complex patterns may be predicted by a theoretical model wherein the exposed surface area of the water bath is minimized. The derivation and solution of this model will be presented in the next talk. (This is part 1 in a 3-talk series).