Snap buckling of a confined thin elastic sheet

TL;DR

This paper investigates the buckling behavior of confined thin elastic sheets, revealing a first-order phase transition influenced by stretchability and providing analytical insights into critical thresholds.

Contribution

It introduces a model that captures the buckling transition in confined elastic sheets, emphasizing the role of compressibility and deriving an analytical expression for the critical threshold.

Findings

Buckling instability is a first-order phase transition.

Critical threshold depends on sheet stretchability.

Compressibility resolves pressure paradox.

Abstract

A growing or compressed thin elastic sheet adhered to a rigid substrate can exhibit a buckling instability, forming an inward hump. Our study shows that the strip morphology depends on the delicate balance between the compression energy and the bending energy. We find that this instability is a first order phase transition between the adhered solution and the buckled solution whose main control parameter is related to the sheet stretchability. In the nearly- unstretchable regime we provide an analytic expression for the critical threshold. Compressibility is the key assumption which allows us to resolve the apparent paradox of an unbounded pressure exerted on the external wall by a confined flexible loop.