A structural gradient theory of torsion, the effects of pretwist, and the tension of pre-twisted DNA

A structural gradient theory of torsion of thin-walled beams is developed. A non-local estimate of the mean value of the angle of twist of the beam leads to a shear gradient that is energetically consistent with a bi-moment, in the spirit of the averaging theory of Vardoulakis and Giannakopoulos (2006). The geometric details of the cross section play the role of the microstructure of the beam, introducing a size effect in the torsion problem. The appropriate boundary conditions are derived from the variational formulation of the problem. The proposed gradient elasticity theory is identical to Vlasov’s torsion theory of thin walled elastic beams. The tension of pre-twisted DNA is analyzed at high axial loads, where enthalpic elasticity prevails. A size effect is naturally introduced, indicating that shorter DNA lengths lead to stiffer response in torsion. It is shown also that the complete unwinding of DNA triggers the debonding of its strands.