Indentation of a floating elastic sheet: Geometry versus applied tension

TL;DR

This paper investigates how a floating elastic sheet responds to indentation, analyzing the effects of applied tension and bending stiffness on force response, wrinkling instability, and comparing theoretical predictions with experiments.

Contribution

It provides a theoretical framework for understanding indentation behavior and wrinkling in floating elastic sheets, including experimental validation and comparison with highly bendable membranes.

Findings

Force-indentation is linear at small depths.

Wrinkling occurs at a critical indentation depth.

Theoretical predictions match experimental results.

Abstract

The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force--indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations the force--indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes.