Measuring the Transition from Wrinkles to Crumples in Stamped Thin Sheets

Abstract

A sufficiently thin elastic solid will exhibit changes in its topography when it is confined to a spherical curvature. As the severity of this curvature is increased, a transition from a wrinkled topography (smooth and undulating) to a crumpled topography (sharp and geometric) occurs in the sheet. Previous experiments that examined this transition featured settings where a tensional load at the sheet’s boundaries allowed it to be constrained to a curvature. However, it is not known what criteria govern this transition in a sheet without a tensional load at its boundaries.

Here, we show that the point of transition from wrinkles to crumples in a thin sheet without boundary tension depends on the sheet’s thickness, the sheet’s diameter, and the imposed radius of curvature. This was investigated by using a pair of curved glass lenses to stamp a thin sheet placed between them, and the point of transition between wrinkles and crumples is represented as the distance between the lenses at which this transition occurs. We propose an empirical threshold to predict this distance based on the aforementioned parameters. This work adds to a better understanding of topographical deformations in thin sheets, which can both lead to degradation of technologies that utilize such a design and be exploited as an engineering tool for applications such as studying cell mechanics and controlling surface microfluidics.