Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

• We study the axial compression of an elastic sheet sliding on a cylindrical substrate.
• The sheet always buckles into one symmetric fold, permitting no periodic solution.
• Upon further compression, the sheet tips over into a recumbent fold.
• The fold remains stable also in the absence of compressive forces.
• Theory and experiments with neoprene sheets are in excellent agreement.

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.