Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains

Abstract

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the transition zone in the merging of two wrinkles, as building-blocks of the global pattern. Contrary to the case of crumple paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work. This formalism is validated from hundreds of nm for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.

7 pages, 4 figures, added references, submitted for publication

References in corpus (11)

• Electric Field Effect in Atomically Thin Carbon Films
• Ripple Texturing of Suspended Graphene Atomic Membranes
• Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Geometry, mechanics and electronics of singular structures and wrinkles in graphene
• Properties of Ridges in Elastic Membranes
• A smooth cascade of wrinkles at the edge of a floating elastic film
• Indium-Gallium Segregation in CuIn${}_x$Ga${}_{1-x}$Se${}_2$: An ab initio based Monte Carlo Study
• Elastic building blocks for confined sheets
• Persistence of a pinch in a pipe
• Period fissioning and other instabilities of stressed elastic membranes

Cited by in corpus (33)

• The Effect of Intrinsic Crumpling on the Mechanics of Free-Standing Graphene
• Initial rigid response and softening transition of highly stretchable kirigami sheet materials
• Strain superlattices and macroscale suspension of Graphene induced by corrugated substrates
• Creating One-dimensional Nanoscale Periodic Ripples in a Continuous Mosaic Graphene Monolayer
• Hierarchy of Graphene Wrinkles Induced by Thermal Strain Engineering
• Hidden area and mechanical nonlinearities in freestanding graphene
• Graphene's morphology and electronic properties from discrete differential geometry
• Wrinkles and folds in a fluid-supported sheet of finite size
• Thermalized buckling of isotropically compressed thin sheets
• Quantitative Chemistry and the Discrete Geometry of Conformal Atom-Thin Crystals
• Formation of wrinkles on graphene induced by nanoparticles: atomic force microscopy study
• Tension-dependent transverse buckles and wrinkles in twisted elastic sheets
• Energy Bounds for a Compressed Elastic Film on a Substrate
• Electric field-controlled rippling of graphene
• Elastic stabilisation of wrinkles in thin films by auxetic microstructure
• Tensional twist-folding of sheets into multilayered scrolled yarns
• Wrinkling of a thin circular sheet bonded to a spherical substrate
• Strain tensor selection and the elastic theory of incompatible thin sheets
• Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases
• Boundary Curvature Effect on the Wrinkling of Thin Suspended Films
• Pattern transitions in a compressible floating elastic sheet
• Nambu-Goldstone modes and diffuse deformations in elastic shells
• Anisotropic neutron star crust, solar system mountains, and gravitational waves
• Second Order Phase Transition and Universality of Self-Buckled Elastic Slender Columns
• Wrinkling and developable cones in centrally confined sheets
• Faceted wrinkling by contracting a curved boundary
• Transition to stress focusing for locally curved sheets
• Sarong rolled around a body demonstrates the force for separating two sheets joined by folding and rolling is very large
• Interplay of gross and fine structures in strongly-curved sheets
• Two Channel Kondo behavior in the quantum XX chain with a boundary defect
• Hysteretic wavelength selection in isometric, unsupported radial wrinkling
• Wrinkles, rucks, and folds formed in a heavy sheet on a frictional surface
• Spontaneous surface reserve formation in wicked membranes bestow extreme stretchability