Minimal resonances in annular non-Euclidean strips

Bryan Gin Ge Chen, Christian D. Santangelo

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of "conical" closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. We derive and test a surprising resonance condition for strips with minimal bending energy along the strip center line to exist.

Original languageEnglish (US)
Article number056601
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume82
Issue number5
DOIs
StatePublished - Nov 2 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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