Wrinkles and folds in a fluid-supported sheet of finite size

Abstract

A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength $\lambda$. As the confinement increases, the deformation energy is progressively localized into a single narrow fold. An exact solution for the deformation of an infinite sheet was previously found, indicating that wrinkles in an infinite sheet are unstable against localization for arbitrarily small confinement. We present an extension of the theory to sheets of finite length $L$, accounting for the experimentally observed wrinkle-to-fold transition. We derive an exact solution for the periodic deformation in the wrinkled state, and an approximate solution for the localized, folded state. We show that a second-order transition between these two states occurs at a critical confinement ${\Delta }_F={\lambda }^2/L$.

arXiv comment15 pages

References in corpus (17)

• Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators
• Elasticity of an interfacial particle raft
• Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains
• A smooth cascade of wrinkles at the edge of a floating elastic film
• Compression induced folding of a sheet: an integrable system
• Folding Langmuir Monolayers
• 3-dimensional structure of a sheet crumpled into a ball
• Morphological Phases of Crumpled Wire
• Elastic building blocks for confined sheets
• Period fissioning and other instabilities of stressed elastic membranes
• Microscopic Wrinkles on Supported Surfactant Monolayers
• Energy distributions and effective temperatures in the packing of elastic sheets
• 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
• Elasto-capillary meniscus: Pulling out a soft strip sticking to a liquid surface
• Measuring order in the isotropic packing of elastic rods

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• Mechanical Self-Assembly of a Strain-Engineered Flexible Layer: Wrinkling, Rolling, and Twisting
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