Experiments on snap buckling, hysteresis and loop formation in twisted rods
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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.
- Coyne, J., “Analysis of the Formation and Elimination of Loops in Twisted Cable,”IEEE Journal of Oceanic Engineering,15(2),72–83 (1990). CrossRef
- 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).
- Rosenthal, F., “The Application of Greenhill's Formulae to Cable Hockling,”ASME Journal of Applied Mechanics,43,681–683 (1976).
- 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).
- Yabuta, T., “Submarine Cable Kink Analysis”Bulletin of the Japanese Society of Mechanical Engineers,27 (231),1821–1828 (1984).
- Hearle, J.W.S. andYegin, A.E., “The Snarling of Highly Twisted Monofilaments,”Journal of the Textile Institute,63 (9),477–489 (1972). CrossRef
- 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).
- 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). CrossRef
- Calladine, C.R., Drew, H., Luisi, B., andTravers, A., Understanding DNA: The Molecule and How It Works, 3rd edition, Elsevier Academic, London (2004).
- Born, M., “Untersuchungenüber die Stabilität der elastischen linie in Ebene und Raum,” Ph.D. Thesis,University of Göttingen, Germany (1906).
- Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, 4th edition, Cambridge University Press, Cambridge (1927).
- 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).
- 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). CrossRef
- 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). CrossRef
- 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). CrossRef
- Kauffman, G.B. andMayo, I., “The Story of Nitinol: The Serendipitious Discovery of the Memory Metal and Its Applications”The Chemical Educator,2 (2),1–21 (1996). CrossRef
- Pemble, C.M. andTowe, B.C., “A Miniature Memory Alloy Pinch Valve,”Sensors and Actuators,77,145–148 (1999). CrossRef
- 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). CrossRef
- Kusy, R.P., “Orthodontic Biomaterials: From the Past to the Present,”Angle Orthodontist,72 (6),501–502 (2002).
- Gere, J.M. andTimoshenko, S.P., Mechanics of Materials, 2nd edition, Van Nostrand Reinhold, London (1987).
- 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). CrossRef
- 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). CrossRef
- Antman, S.S., Nonlinear Problems of Elasticity, Springer-Verlag, New York (1995).
- Kehrbaum, S. andMaddocks, J.H., “Elastic Bodies, Quarternians and the Last Quadrature,”Proceedings of the Royal Society of London,A355,2117–2136 (1997).
- 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).
- Euler, L., “Additamentum 1 de curvis elasticis, methodus inveniendi lineas curvas maximi minimivi proprietate gaudentes”Bousquent, Lausanne (1744). Reprinted in Opera Omnia I,24,231–297.
- Zajac, E.E., “Stability of Two Planar Loop Elasticas,”Transactions of the ASME Journal of Applied Mechanics,29,136–142 (1962).
- Experiments on snap buckling, hysteresis and loop formation in twisted rods
Volume 45, Issue 2 , pp 101-111
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- Twisted rods
- rod experiments
- snap buckling
- loop formation
- welded boundary conditions
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