Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate
arXiv:1503.05030 · doi:10.1016/j.ijnonlinmec.2015.02.013
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.
arXiv comment20 pages, 5 figures
References in corpus (9)
- Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators
- Compression induced folding of a sheet: an integrable system
- Contact lines for fluid surface adhesion
- Statics and inertial dynamics of a ruck in a rug
- The Shape and Motion of a Ruck in a Rug
- Growth-induced blisters in a circular tube
- Shape and symmetry of a fluid-supported elastic sheet
- Non-symmetric localized fold of a floating sheet
- Mechanics of large folds in thin interfacial films