Incomplete contacts in partial slip subject to varying normal and shear loading, and their representation by asymptotes

We develop a method for the solution of partial slip contact problems suffering complex loading cycles where, generally, the normal load, shear force and, potentially, differential bulk tensions are all functions of time, using an edge-asymptote approach. The size of the slip zone and local shear traction distribution are revealed as functions of time. The results are then re-worked in asymptotic form, so that they do not hinge on inherent symmetry and anti-symmetry conditions for the contact overall, and are of general applicability. The multipliers on the local solutions (generalised stress intensity factors) are also appropriate as a means of taking laboratory tests quantifying fretting fatigue and employing them to wholly different prototypical problems.