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 clamped-clamped 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 tension-torsion coupling has a pronounced influence on the computed looped geometries. This finding has implications for DNA loops formed by DNA-protein binding as well as loop formation in helically wound wire and synthetic cables.