title: Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets.
abstract: Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles--their wavelength--is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, MA 01003; Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003;
authors.forename: Joseph D
authors.identifier: http://orcid.org/0000-0001-6048-456X
authors.initials: JD
authors.lastname: Paulsen
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, MA 01003;
authors.forename: Evan
authors.initials: E
authors.lastname: Hohlfeld
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, MA 01003;
authors.forename: Hunter
authors.initials: H
authors.lastname: King
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, MA 01003; Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003;
authors.forename: Jiangshui
authors.initials: J
authors.lastname: Huang
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, MA 01003;
authors.forename: Zhanlong
authors.initials: Z
authors.lastname: Qiu
authors.affiliation: Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003;
authors.forename: Thomas P
authors.initials: TP
authors.lastname: Russell
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, MA 01003; bdavidov@physics.umass.edu menon@physics.umass.edu dominic.vella@maths.ox.ac.uk.
authors.forename: Narayanan
authors.initials: N
authors.lastname: Menon
authors.affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom bdavidov@physics.umass.edu menon@physics.umass.edu dominic.vella@maths.ox.ac.uk.
authors.forename: Dominic
authors.initials: D
authors.lastname: Vella
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, MA 01003; bdavidov@physics.umass.edu menon@physics.umass.edu dominic.vella@maths.ox.ac.uk.
authors.forename: Benny
authors.initials: B
authors.lastname: Davidovitch
keywords: curved topography; elastic sheets; wrinkles