Frictional shakedown in a complete contact

The phenomenon of frictional shakedown is investigated by considering a complete contact configuration for which a stable partial slip regime exists; a tilted square-ended rigid punch is pressed against an incompressible half-plane by an offset constant normal load and subject to an oscillatory shearing force. The analysis shows that analogies might be drawn with conventional plasticity nomenclature and that, under certain conditions, Melan's lower bound theorem of plastic shakedown may be invoked, leading to the elimination of steady state slip. The implications of these results to fretting contacts are discussed.