A collaboration led by Dr Rehan Shah in conjunction with UCL academic Prof Gert van der Heijden has resulted in a publication in the reputed Journal of the Mechanics and Physics of Solids (JMPS) and is available as an open access paper on http://dx.doi.org/10.1016/j.jmps.2023.105224.

In this paper, a comprehensive geometrically-exact theory for an end-loaded elastic rod constrained to deform on a cylindrical surface is developed. By viewing the rod-cylinder system as a special case of an elastic braid, all forces and moments imparted by the deforming rod to the cylinder as well as all contact reactions are able to be obtained. This framework enables a complete treatment of static friction consistent with force and moment balance.

In addition to the commonly considered model of hard frictionless contact, two friction models in which the rod, possibly with intrinsic curvature, experiences either lateral or tangential friction, are analysed in detail. As applications of the theory the buckling of the constrained rod under compressive and torsional loads is studied to find critical loads depending on Coulomb-like friction parameters, as well as the tendency of the rod to lift off the cylinder under further loading. The results are relevant for many engineering and medical applications in which a slender structure winds inside or outside a cylindrical boundary.

Updated by: Rehan Shah