Wrinkling and imaging of thin curved sheets

TL;DR

This paper introduces a non-invasive imaging method to study wrinkling patterns on curved thin sheets, revealing how curvature influences instability features and validating theoretical models with practical implications.

Contribution

It develops a robust schlieren imaging technique for curved sheets and evaluates the impact of Gaussian curvature on wrinkling, comparing results with recent theories.

Findings

Gaussian curvature significantly affects wrinkle wavelength and amplitude.

The imaging method accurately reconstructs surface topography of wrinkling sheets.

Model assumptions about surface area conservation need careful consideration.

Abstract

Thin films or sheets subjected to external forces often undergo mechanical instability, leading to regular patterns of wrinkles, folds, and creases. As can be anticipated from the difficulty of flattening a curved globe, any natural curvature of the sheet will have a strong influence on these instabilities. Here, we develop a non-invasive synthetic schlieren imaging technique to image and reconstruct the surface of wrinkling curved sheets, confined to float on water. Our method circumvents the small-amplitude limit of related imaging techniques, and we demonstrate robust means to estimate the reconstruction accuracy. We then evaluate how the sign and magnitude of Gaussian curvature affects the wrinkling of thin curved sheets, and compare observations of the wrinkle wavelength, amplitude and domain structure with recent theoretical predictions. While generally validating model predictions, we find that the assumption of a conserved surface area during wrinkling should be treated with some care. The control of wrinkling behavior demonstrated here can have application in the design of liquid lenses, microfluidics, active textured surfaces, and flexible electronic components.