The Wrinkling of a Twisted Ribbon

Robert V. Kohn, Ethan O’Brien

Research output: Contribution to journalArticle

Abstract

Recent experiments by Chopin and Kudrolli (Phys Rev Lett 111:174302, 2013) showed that a thin elastic ribbon, when twisted into a helicoid, may wrinkle in the center. We study this from the perspective of elastic energy minimization, building on recent work by Chopin et al. (J Elast 119(1–2):137–189, 2015) in which they derive a modified von Kármán functional and solve the relaxed problem. Our main contribution is to show matching upper and lower bounds for the minimum energy in the small-thickness limit. Along the way, we show that the displacements must be small where we expect that the ribbon is helicoidal, and we estimate the wavelength of the wrinkles.

Original languageEnglish (US)
Pages (from-to)1221-1249
Number of pages29
JournalJournal of Nonlinear Science
Volume28
Issue number4
DOIs
StatePublished - Aug 1 2018

Keywords

  • Energy scaling laws
  • Microstructure
  • Thin elastic sheets
  • Wrinkling

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

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