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

Abstract

We study three-dimensional deformations of thin inextensible elastic rods with non-vanishing spontaneous curvature and torsion. In addition to the usual description in terms of curvature and torsion which considers only the configuration of the centerline of the rod, we allow deformations that involve the rotation of the rod's cross-section around its centerline. We derive new expressions for the mechanical energy and for the force and moment balance conditions for the equilibrium of a rod under the action of arbitrary external loads. Several illustrative examples are studied and the connection between our results and recent experiments on stretching of supercoiled DNA molecules is discussed.