Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables
The paper contributes a general dynamical formulation and numerical solution procedure for studying nonlinear and three-dimensional dynamics of Kirchhoff rods. Target applications include the dynamic formation of DNA loops and supercoils as well as loops (hockles) in marine cables. The formulation accommodates non-homogeneous and non-isotropic inextensible rods both with and without coupling of tension and torsion. The utility of this formulation is illustrated by studying the dynamics and quasi-static response of a clampedclamped rod subject to compression and/or twist. For slow loading rates, the computed quasi-static responses converge to published equilibrium solutions for a benchmark problem. As loading rates increase, new behaviors are observed including hysteresis in the neighborhood of equilibrium bifurcations. The addition of chirality in the form of tensiontorsion coupling has a pronounced influence on the computed looped geometries. This finding has implications for DNA loops formed by DNAprotein binding as well as loop formation in helically wound wire and synthetic cables.
dynamics looping kirchhoff rod supercoiling cable mechanics dna mechanics