Instability and self-contact phenomena in the writhing of clamped rods

John Michael Tutill Thompson, G. H. M. Van Der Heijden, S. Neukirch, V. G. A. Goss

Research output: Contribution to journalArticle

86 Citations (Scopus)

Abstract

We use the Cosserat rod theory to present a unified picture of jump phenomena, associated with looping, snap-through, pop-out, etc., in twisted clamped rods undergoing large deflections. Both contact-free rods and rods with isolated points of self-contact are considered. Taking proper account of the symmetries of the problem we find that an arbitrary contact-free solution is fully characterised by four parameters; each point contact adds another two. A shooting method is used for solving the boundary value problem. An intricate bifurcation picture emerges with a strong interplay between planar and spatial rod configurations. We find new jump phenomena by treating the ratio of torsional to bending stiffness of the rod as a bifurcation parameter. Load-deflection curves are computed and compared with results from carefully conducted experiments on contact-free as well as self-contacting metal-alloy rods. (C) 2003 Elsevier Science Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)161-196
Number of pages35
JournalInternational Journal of Mechanical Sciences
Volume45
Issue number1
DOIs
Publication statusPublished - Jan 2003

Keywords

  • cosserat rod
  • clamped boundary conditions
  • end rotation, (out-of-plane) buckling
  • instability
  • bifurcation
  • self-contact
  • looping
  • snap-through
  • pop-out
  • experiments
  • SUPERCOILED DNA MOLECULE
  • NONLINEARLY ELASTIC RODS
  • TWISTED RODS
  • STABILITY
  • PLASMIDS
  • COLLAPSE
  • BEHAVIOR
  • LENGTH
  • RINGS
  • CABLE

Cite this

Thompson, J. M. T., Van Der Heijden, G. H. M., Neukirch, S., & Goss, V. G. A. (2003). Instability and self-contact phenomena in the writhing of clamped rods. International Journal of Mechanical Sciences, 45(1), 161-196. https://doi.org/10.1016/S0020-7403(02)00183-2