Plane incomplete contact problems subject to bulk stress with a varying normal load

In the case of a general symmetric incomplete contact, if we can deduce the partial slip solution when it is subjected first to a normal load (held constant) and then to a monotonically increasing bulk tension, we show, here, how to obtain the solution when the normal load and bulk tension vary with time in an arbitrary manner. The procedure is demonstrated for a Hertzian contact where the constant normal load solution is known in closed form. It reveals the extent of slip and the shear traction distribution at all points within the contact at any instant. It was discovered that the size of the permanent stick zone, for a given cyclic loading trajectory, is unique in the steady state. The steady state is established after one cycle of loading: it is independent of the transient loading prior to reaching the steady state cycle, which is also observed in the case of varying normal and shear loading (P−Q). An example is given to illustrate the type of behaviour that is to be expected.