Experimental Mechanics

, 45:101

Experiments on snap buckling, hysteresis and loop formation in twisted rods

  • V. G. A. Goss
  • G. H. M. van der Heijden
  • J. M. T. Thompson
  • S. Neukirch
Article

Abstract

We give the results of large deflection experiments involving the bending and twisting of 1 mm diameter nickel-titanium alloy rods, up to 2 m in length. These results are compared to calculations based on the Cosserat theory of rods. We present details of this theory, formulated as a boundary value problem. The mathematical boundary conditions model the experimental setup. The rods are clamped in aligned chucks and the experiments are carried out under rigid loading conditions. An experiment proceeds by either twisting the ends of the rod by a certain amount and then adjusting the slack, or fixing the slack and varying the amount of twist. In this way, commonly encountered phenomena are investigated, such as snap buckling, the formation of loops, and buckling into and out of planar configurations. The effect of gravity is discussed.

Key Words

Twisted rods rod experiments snap buckling loop formation snarling hockling welded boundary conditions nitinol bifurcation 

References

  1. 1.
    Coyne, J., “Analysis of the Formation and Elimination of Loops in Twisted Cable,”IEEE Journal of Oceanic Engineering,15(2),72–83 (1990).CrossRefGoogle Scholar
  2. 2.
    Liu, F.C., “Kink Formation and Rotational Response of Single and Multistrand Electromechanical Cables,”Technical Note N-1403, Civil Engineering Lab, Naval Construction Batallion Center, Port Hueneme, CA (1975).Google Scholar
  3. 3.
    Rosenthal, F., “The Application of Greenhill's Formulae to Cable Hockling,”ASME Journal of Applied Mechanics,43,681–683 (1976).Google Scholar
  4. 4.
    Tan, Z. andWitz, J.A., “Loop Formation of Marine Cables and Umbilicals During Installation,”Proceedings of Behaviour of Offshore Structures (BOSS '92), London, UK, Vol. II,M.H. Patel andR. Gibbins (editors),BPP Technical Services, London, 1270–1285 (1992).Google Scholar
  5. 5.
    Yabuta, T., “Submarine Cable Kink AnalysisBulletin of the Japanese Society of Mechanical Engineers,27 (231),1821–1828 (1984).Google Scholar
  6. 6.
    Hearle, J.W.S. andYegin, A.E., “The Snarling of Highly Twisted Monofilaments,”Journal of the Textile Institute,63 (9),477–489 (1972).CrossRefGoogle Scholar
  7. 7.
    Swigon, D., “Configurations With Self-contact in the Theory of the Elastic Rod Model for DNA,” Ph.D. Dissertation,Rutgers State University of New Jersey, NJ (1999).Google Scholar
  8. 8.
    Coleman, B.D. andSwigon, D., “Theory of Supercoiled Elastic Rings with Self-contact and Its Application to DNA Plasmids,”Journal of Elasticity,60,173–221 (2000).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Calladine, C.R., Drew, H., Luisi, B., andTravers, A., Understanding DNA: The Molecule and How It Works, 3rd edition, Elsevier Academic, London (2004).Google Scholar
  10. 10.
    Born, M., “Untersuchungenüber die Stabilität der elastischen linie in Ebene und Raum,” Ph.D. Thesis,University of Göttingen, Germany (1906).Google Scholar
  11. 11.
    Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, 4th edition, Cambridge University Press, Cambridge (1927).MATHGoogle Scholar
  12. 12.
    Greenhill, A.G., “On the Strength of Shafting When Exposed Both to Torsion and to End Thrust,” Proceedings of the Institute of Mechanical Engineers, London, April, 182–209 (1883).Google Scholar
  13. 13.
    Thompson, J.M.T. andChampneys, A.R., “From Helix to Localized Writhing in the Torsional Post-buckling of Elastic Rods,”Proceedings of the Royal Society of London A452,117–138 (1996).MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Miyazaki, Y. andKondo, K., “Analytical Solution of Spatial Elastica and Its Application to Kinking Problem,”International Journal of Solids and Structures,34 (27),3619–3636 (1997).MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Van der Heijden, G.H.M., Neukirch, S., Goss, V.G.A., andThompson, J.M.T., “Instability and Contact Phenomena in the Writhing of Clamped Rods,”International Journal of Mechanical Sciences,45,161–196 (2003).CrossRefMATHGoogle Scholar
  16. 16.
    Kauffman, G.B. andMayo, I., “The Story of Nitinol: The Serendipitious Discovery of the Memory Metal and Its ApplicationsThe Chemical Educator,2 (2),1–21 (1996).CrossRefGoogle Scholar
  17. 17.
    Pemble, C.M. andTowe, B.C., “A Miniature Memory Alloy Pinch Valve,”Sensors and Actuators,77,145–148 (1999).CrossRefGoogle Scholar
  18. 18.
    Kujala, S., Pajala, A., Kallioinen, M., Pramila, A., Tuukkanen, J., andRyhanen, J., “Biocompatibility and Strength Properties of Nitinol Shape Memory Alloy Suture in Rabbit Tendon,”Biomaterials,25,353–358 (2004).CrossRefGoogle Scholar
  19. 19.
    Kusy, R.P., “Orthodontic Biomaterials: From the Past to the Present,”Angle Orthodontist,72 (6),501–502 (2002).Google Scholar
  20. 20.
    Gere, J.M. andTimoshenko, S.P., Mechanics of Materials, 2nd edition, Van Nostrand Reinhold, London (1987).Google Scholar
  21. 21.
    Rucker, B.K. andKusy, R.P., “Elastic Properties of Alternative Versus Single Stranded Leveling Archwires,”American Journal of Orthodontics and Dentofacial Orthopedics,122 (5),528–541 (2002).CrossRefGoogle Scholar
  22. 22.
    Drake, S.R., Wayne, D.M., Powers, J.M., andAsgar, K., “Mechanical Properties of Orthodontic Wires in Tension, Bending, and Torsion,”American Journal of Orthodontics,82 (3),206–210 (1982).CrossRefGoogle Scholar
  23. 23.
    Antman, S.S., Nonlinear Problems of Elasticity, Springer-Verlag, New York (1995).MATHGoogle Scholar
  24. 24.
    Kehrbaum, S. andMaddocks, J.H., “Elastic Bodies, Quarternians and the Last Quadrature,”Proceedings of the Royal Society of London,A355,2117–2136 (1997).MathSciNetMATHGoogle Scholar
  25. 25.
    Shampine, L.W., Kierzenka, J., and Reichelt, M.W., “Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB with bvp4c,” ftp://ftp.mathworks.com/pub/doc/papers/bvp/ (2000).Google Scholar
  26. 26.
    Euler, L., “Additamentum 1 de curvis elasticis, methodus inveniendi lineas curvas maximi minimivi proprietate gaudentesBousquent, Lausanne (1744). Reprinted in Opera Omnia I,24,231–297.Google Scholar
  27. 27.
    Zajac, E.E., “Stability of Two Planar Loop Elasticas,”Transactions of the ASME Journal of Applied Mechanics,29,136–142 (1962).MATHMathSciNetGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2005

Authors and Affiliations

  • V. G. A. Goss
    • 1
    • 2
  • G. H. M. van der Heijden
    • 1
  • J. M. T. Thompson
    • 1
  • S. Neukirch
    • 1
  1. 1.Centre for Nonlinear DynamicsUniversity College LondonLondonUK
  2. 2.currently at London South Bank UniversityLondonUK

Personalised recommendations