Wrapping an adhesive sphere with a sheet

TL;DR

This paper investigates how an elastic sheet adheres to a spherical surface, revealing various contact patterns driven by the interplay of bending, stretching, and adhesion energies, and presents a comprehensive diagram of these morphologies.

Contribution

It introduces a systematic analysis of adhesion-induced morphologies of elastic sheets on spheres, linking geometric and material parameters to observed patterns.

Findings

Multiple contact patterns identified, from disks to branched shapes.

A configuration diagram mapping morphologies to energy ratios.

Demonstrates the role of metric distortions in adhesion phenomena.

Abstract

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss'Theorema Egregium shows that this operation necessarily generates metric distortions (i.e. stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two non-dimensional parameters comparing respectively bending and stretching energies to adhesion. A complete configuration diagram is finally proposed.