  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.
