Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets

Proceedings of the National Academy of Sciences of the United States of America
Joseph D PaulsenBenny Davidovitch

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.

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Citations

Apr 5, 2017·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Peter Bella, Robert V Kohn
Apr 5, 2017·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Matteo Taffetani, Dominic Vella
Apr 19, 2018·Soft Matter·Tero KämäräinenOrlando J Rojas
May 16, 2018·Soft Matter·Benny Davidovitch, Dominic Vella
Dec 9, 2017·Physical Review Letters·S KarpitschkaJ H Snoeijer
Sep 5, 2018·Soft Matter·Timothy TwohigAndrew B Croll
Nov 10, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·Finn BoxJerome A Neufeld
Aug 9, 2019·Soft Matter·Kirsten HarthRalf Stannarius
Jan 23, 2020·Soft Matter·H BenseJ Bico
Mar 23, 2018·The European Physical Journal. E, Soft Matter·Benjamin Davis-PurcellKari Dalnoki-Veress
Dec 29, 2018·Proceedings of the National Academy of Sciences of the United States of America·Benny DavidovitchGregory M Grason
May 22, 2019·Physical Review. E·Leonardo Gordillo, Edgar Knobloch
Dec 25, 2019·Physical Review. E·Andreea PanaitescuArshad Kudrolli
Feb 9, 2018·Soft Matter·Cheng ZhangHuajian Gao
Aug 17, 2018·Physical Review. E·Dominic Vella, Benny Davidovitch
Oct 3, 2019·Physical Review. E·Madison S Krieger, Marcelo A Dias
Oct 2, 2019·Proceedings of the National Academy of Sciences of the United States of America·Finn BoxDominic Vella
Feb 12, 2017·Physical Review Letters·Joseph D PaulsenNarayanan Menon
Feb 13, 2020·Proceedings of the National Academy of Sciences of the United States of America·Oleh TovkachBenny Davidovitch
Jul 19, 2017·Nature Communications·Hillel AharoniEleni Katifori
Jan 23, 2021·Soft Matter·Alexander GreinerSilvia Budday
Apr 2, 2021·Proceedings of the National Academy of Sciences of the United States of America·Pablo AresKostya S Novoselov
May 13, 2021·Soft Matter·Andrei Zakharov, Kinjal Dasbiswas
May 20, 2021·Physical Review. E·Benny Davidovitch, Francisco Guinea
Jun 24, 2021·The European Physical Journal. E, Soft Matter·Andrei Zakharov, Kinjal Dasbiswas
Apr 25, 2020·Nano-micro Letters·Yinlong TanWenjian Wu
Jul 10, 2021·The European Physical Journal. E, Soft Matter·Meng Xin, Benny Davidovitch
Apr 21, 2020·Journal of the American Chemical Society·Shir R LiberEli Sloutskin
Nov 30, 2021·Soft Matter·Christoph KloppRalf Stannarius

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