  The spontaneous formation of double helices for filaments under torsion is
common and significant. For example, the research on the supercoiling of DNA is
helpful for understanding the replication and transcription of DNA. Similar
double helices can appear in polymer chains, carbon nanotube yarns, cables,
telephone wires and so forth. We noticed that non-uniform double helices can be
produced due to the surface friction induced by the self-contact. Therefore an
ideal model was presented to investigate the formation of double helices for
elastic rods under torque. A general equilibrium condition which is valid for
both the smooth surface and the rough surface situations is derived by using
the variational method. Based on this, by adding further constraints, the
smooth and rough surface situations are investigated in detail respectively.
Additionally, the model showed that the specific process of how to twist and
slack the rod can determine the surface friction and hence influence the
configuration of the double helix formed by rods with rough surfaces. Based on
this principle, a method of manufacturing double helices with designed
configurations was proposed and demonstrated. Finally, experiments were
performed to verify the model and the results agreed well with the theory.
