Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

TL;DR

This paper investigates the buckling behavior of a soft elastic sheet on a cylindrical substrate, revealing a transition from symmetric to asymmetric folds under compression, supported by theoretical predictions and experimental validation.

Contribution

It introduces a new understanding of buckling modes in cylindrical systems, showing the stability of a single symmetric fold and the transition to a recumbent fold with compression.

Findings

The sheet buckles into a single symmetric fold under axial compression.

Further compression causes symmetry breaking and formation of a recumbent fold.

Theoretical predictions closely match experimental results.

Abstract

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.