Nonlinear dynamic intertwining of rods with self-contact

TL;DR

This paper models the complex dynamic behavior of twisted rods with self-contact, revealing how they evolve from straight to intertwined loops, with applications to marine cables and DNA supercoiling.

Contribution

It introduces a computational rod model that explicitly accounts for dynamic self-contact, providing new insights into the evolution of intertwined rods under twisting.

Findings

Rod evolves from straight to intertwined loops under twist.

Self-contact leads to complex intertwining behavior.

Energy conversion from torsion to bending and writhe is key.

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