Multiple helical perversions of finite, intristically curved rods

G. Domokos, T. J. Healey

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We investigate mechanical spatial equilibria of slender elastic rods with intristic curvature. Our work is, to some extent, motivated by papers [Goriely & Tabor, 1998; Goriely & McMillen, 2002]. There such rods of infinite length were recently studied to quantify the behavior of botanical filaments. In particular, an adequate explanation for the existence of helical perversions (the transition between helical segments of opposite handedness) is provided in [Goriely &: Tabor, 1998]. However, this theory fails to describe multiple perversions, which can be observed in Nature. In contrast we formulate a two-point boundary-value problem describing rods of finite length with initial curvature and clamped ends. We identify trivial solutions as straight configurations and also κ-covered circles, rigorously establish the existence of local bifurcations, and then compute global solutions via the Parallel Hybrid Algorithm [Domokos & Szeberényi, 2004] to find spatially complex equilibria characterized by multiple perversions. Based on computational results and the White-Fuller theorem [White, 1969; Fuller, 1971; Calugareanu, 1961] we describe a heuristic global picture of the bifurcation diagram, which can serve as an explanation for the evolution of physically observable tendril shapes.

Original languageEnglish
Pages (from-to)871-890
Number of pages20
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume15
Issue number3
DOIs
Publication statusPublished - Mar 2005

Keywords

  • Bifurcations
  • Botanical tendrils
  • Helical perversion
  • Intristic curvature
  • Rod theory

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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