Planar sheets meet negative curvature liquid interfaces

TL;DR

This paper investigates how inextensible thin sheets adhere to negatively curved liquid interfaces, analyzing resulting stress, and predicting the formation of wrinkles or folds based on substrate curvature through analytic and numerical methods.

Contribution

It provides a detailed analysis of geometric frustration in thin sheets on negatively curved surfaces, identifying conditions for different folding patterns and mapping their phase diagram.

Findings

Concentric wrinkles and eye-like folds are compatible with negative Gaussian curvature.

The pattern formed depends on the substrate's curvature.

A phase diagram predicts the occurrence of different folding patterns.

Abstract

If an inextensible thin sheet is adhered to a substrate with a negative Gaussian curvature it will experience stress due to geometric frustration. We analyze the consequences of such geometric frustration using analytic arguments and numerical simulations. Both concentric wrinkles and eye-like folds are shown to be compatible with negative curvatures. Which pattern will be realized depends on the curvature of the substrate. We discuss both types of folding patterns and determine the phase diagram governing their appearance.