Instability and self-contact phenomena in the writhing of clamped rods
By G. H. M. Heijden, Sebastien Neukirch, V. Goss, J. Michael T. Thompson. 2003
150 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Mechanical Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/d3dbc330c0e24a0a679fa2cbd8f53f97955916e0
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In Mechanical Engineering
In Mechanics of Materials
Citations in the corpus
- Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables (2005, background): “This number of twists is also referred to as the ‘‘end rotation’’ in [21].”
- Discrete elastic rods (2008, methodology): “Mathematical analysis, modeling, and simulation of elastic rods is an active field in mechanics [van der Heijden et al. 2003; Goyal et al. 2007], numerical analysis [Falk and Xu 1995], and geometry [Bobenko and Suris 1999; Lin and Schwetlick 2004] with applications spanning medicine [Lenoir et al.…”