Torsional contact of an elastic flat-ended cylinder

Torsion of a flat-ended elastic bar pressed onto an elastically similar half-space and subject to torsion, in the presence of friction, is used as a vehicle to study complete contact subject to in-plane and anti-plane shearing forces. It is shown that, below a critical coefficient of friction, slip starts at the edge and progress inwards as the torsion is increased, whereas above this critical value slip starts a little way in from the edge and progress both inwards and outwards. Care is taken to preserve frictional orthogonality, with slip modelled as a piecewise-linear distribution of edge and screw dislocations. The solutions may be applied to any complete contact edge, as the problem is solved within the context of a Williams eigenexpansion.