Non-symmetric localized fold of a floating sheet

TL;DR

This paper explores the transition from symmetric to non-symmetric localized folds in an elastic sheet on a liquid surface, generalizing existing solutions and demonstrating their relevance to physical experiments with soft strips.

Contribution

It introduces a continuous family of solutions for localized folds, extending previous symmetric and antisymmetric models to include non-symmetric shapes.

Findings

Non-symmetric fold solutions exist and are mathematically derived.

Non-symmetric shapes are observable in experiments with soft strips.

The generalized solutions unify different fold configurations.

Abstract

An elastic sheet lying on the surface of a liquid, if axially compressed, shows a transition from a smooth sinusoidal pattern to a well localized fold. This wrinkle-to-fold transition is a manifestation of a localized buckling. The symmetric and antisymmetric shapes of the fold have recently been described by Diamant and Witten (2011), who found two exact solutions of the nonlinear equilibrium equations. In this Note, we show that these solutions can be generalized to a continuous family of solutions, which yields non symmetric shapes of the fold. We prove that non symmetric solutions also describe the shape of a soft strip withdrawn from a liquid bath, a physical problem that allows to easily observe portions of non symmetric profiles.