Geometry-driven folding of a floating annular sheet

TL;DR

This paper investigates how an elastic annular sheet floating on water deforms under tension, revealing that shape transitions are governed by geometry and are independent of bending rigidity.

Contribution

It introduces a geometric approach to predict large deformations and buckling transitions of floating elastic sheets, emphasizing shape determination through area extremization.

Findings

Buckling transitions are insensitive to bending rigidity.

Multiple morphologies including folds and wrinkles are observed.

A geometric model explains shape selection and transitions.

Abstract

Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self-contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where an annular polymer sheet floating on an air-water interface is subjected to different tensions on the inner and outer rims. The sheet folds and wrinkles into many distinct morphologies that break axisymmetry. These states can be understood within a recent geometric approach for determining the gross shape of extremely bendable yet inextensible sheets by extremizing an appropriate area functional. Our analysis explains the remarkable feature that the observed buckling transitions between wrinkled and folded shapes are insensitive to the bending rigidity of the sheet.