On the Bending and Twisting of Rods with Misfit

Robert V. Kohn, Ethan O’Brien

Research output: Contribution to journalArticle

Abstract

We derive a one-dimensional variational problem representing the elastic energy of a rod with misfit, starting from a nonlinear, three-dimensional elastic energy with nontrivial preferred strain. Our approach to dimension reduction is to find a Gamma-limit as the thickness of the rod tends to 0. The limiting energy is a quadratic function of the rates at which the rod bends and twists, and we give explicit expressions for the preferred curvature and twist in the special case of isotropic elastic moduli.

Original languageEnglish (US)
Pages (from-to)115-143
Number of pages29
JournalJournal of Elasticity
Volume130
Issue number1
DOIs
StatePublished - Jan 1 2018

Keywords

  • Dimension reduction
  • Elastic rods
  • Gamma-convergence
  • Misfit

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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