Instability and self-contact phenomena in the writhing of clamped rods
G.H.M. van der Heijden, S. Neukirch, V.G.A. Goss & J.M.T. Thompson
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.
keywords: Cosserat rod, clamped boundary conditions, end rotation,
(out-of-plane) buckling, instability, bifurcation, self-contact, looping,
snap-through, pop-out, experiments
Int. J. Mech. Sciences 45, 161-196 (2003)