Dynamic curling of an Elastica: a nonlinear problem in elastodynamics solved by matched asymptotic expansions

B. Audoly, A. Callan-Jones, P. T. Brun

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider the motion of an infinitely long, naturally curved, planar Elastica. The Elastica is flattened onto a rigid impenetrable substrate and held by its endpoints. When one of its endpoints is released, it is set off in a curling motion, which we seek to describe mathematically based on the non-linear equations of motions for planar elastic rods undergoing finite rotations. This problem is used to introduce the technique of matched asymptotic expansions. We derive a non-linear solution capturing the late dynamics, when a roll comprising many turns has formed: in this regime, the roll advances at an asymptotically constant velocity, whose selection we explain. This contribution presents an expanded version of the results published in Callan-Jones et al. (Phys. Rev. Lett. 2012).

Original languageEnglish (US)
Title of host publicationCISM International Centre for Mechanical Sciences, Courses and Lectures
PublisherSpringer International Publishing
Pages137-155
Number of pages19
DOIs
StatePublished - Jan 1 2015
Externally publishedYes

Publication series

NameCISM International Centre for Mechanical Sciences, Courses and Lectures
Volume562
ISSN (Print)0254-1971
ISSN (Electronic)2309-3706

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications

Keywords

  • Constant Curvature
  • Master Curve
  • Matched Asymptotic Expansion
  • Nonlinear Problem
  • Physical Review Letter

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