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Wrapping an adhesive sphere with an elastic sheet.

Jérémy Hure¹, Benoît Roman, José Bico

¹Physique et Mécanique des Milieux Hétérogènes, CNRS UMR 7636, UPMC and Université Paris Diderot, ESPCI-ParisTech, 10 rue Vauquelin, 75231 Paris Cedex 05, France.

Physical Review Letters

|June 4, 2011

Summary

Researchers explored how elastic sheets stick to spheres, finding that the contact shape depends on bending, stretching, and adhesion. This work maps various adhesion patterns based on material and geometric properties.

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Area of Science:

Physics
Materials Science
Applied Mathematics

Background:

Studying the adhesion of elastic materials to curved surfaces is crucial for understanding phenomena in various fields.
Gauss's Theorema Egregium highlights that adhering a flat sheet to a sphere inherently causes stretching and bending due to differing geometries.

Purpose of the Study:

To investigate the diverse contact patterns formed when an elastic sheet adheres to a rigid spherical substrate.
To correlate these patterns with the interplay of geometrical and material properties.

Main Methods:

Analysis of elastic sheet adhesion on a spherical substrate.
Utilizing principles from differential geometry (Gauss's Theorema Egregium) to understand metric distortions.
Developing a model based on nondimensional parameters comparing bending and stretching energies to adhesion.

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Main Results:

Observed a wide range of contact morphologies, from simple disks to complex branched shapes.
Demonstrated that these patterns are a function of geometrical and material properties.
Identified two key nondimensional parameters governing the observed adhesion patterns.

Conclusions:

The adhesion of elastic sheets to spherical substrates results in complex behaviors driven by intrinsic metric distortions.
A comprehensive configuration diagram effectively maps the observed contact patterns based on material and geometric factors.
This study provides a framework for predicting and understanding the adhesion behavior of elastic sheets on curved surfaces.