Elasticity of thin rods with spontaneous curvature and torsion - beyond geometrical lines

摘要

We study three-dimensional deformations of thin inextensible elastic rodswith non-vanishing spontaneous curvature and torsion. In addition to the usualdescription in terms of curvature and torsion which considers only theconfiguration of the centerline of the rod, we allow deformations that involvethe rotation of the rod's cross-section around its centerline. We derive newexpressions for the mechanical energy and for the force and moment balanceconditions for the equilibrium of a rod under the action of arbitrary externalloads. Several illustrative examples are studied and the connection between ourresults and recent experiments on stretching of supercoiled DNA molecules isdiscussed.