Nonlinear dynamic intertwining of rods with self-contact
arXiv:math-ph/0701017 · doi:10.1016/j.ijnonlinmec.2007.10.004
Abstract
Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or hockles are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively by the dynamic conversion of twist (Tw) to writhe (Wr). KEY WORDS Rod Dynamics, Self-contact, Intertwining, DNA Supercoiling, Cable Hockling
35 pages, 9 figures, submitted to Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
References in corpus (3)
Cited by in corpus (6)
- Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments
- Dynamics of elastic rods in perfect friction contact
- Sobolev Gradients for the Möbius Energy
- A symplectic integration method for elastic filaments
- A quaternion-based continuation method to follow the equilibria and stability of slender elastic rods
- Constitutive-law Modeling of Microfilaments from their Discrete-Structure Simulations - A Method based on an Inverse Approach Applied to a Static Rod Model