Static friction models for a rod deforming on a cylinder
R. Shah & G.H.M. van der Heijden
We develop a comprehensive geometrically-exact theory for an end-loaded
elastic rod constrained to deform on a cylindrical surface. By viewing the
rod-cylinder system as a special case of an elastic braid, we are able to
obtain all forces and moments imparted by the deforming rod to the cylinder
as well as all contact reactions. This framework allows us to give a
complete treatment of static friction consistent with force and moment
balance. In addition to the commonly considered model of hard frictionless
contact we analyse in detail two friction models in which the rod, possibly
with intrinsic curvature, experiences either lateral or tangential friction.
As applications of the theory we study buckling of the constrained rod under
compressive and torsional loads, finding critical loads to depend on
Coulomb-like friction coefficients, as well as the tendency of the rod to
lift off the cylinder under further loading. Our results are relevant for
many engineering and medical applications in which a slender structure
winds inside or outside a cylindrical boundary.
keywords: elastic rod, surface constraint, buckling, static friction,
contact pressure, lift-off
J. Mech. Phys. Solids 173, 105224 (2023)