Energy Loss in Frictional Hertzian Contact Subjected to Two-Dimensional Cyclic Loadings

We investigate the effect of three different harmonically varying loads as a function of the friction coefficient on energy loss in a three-dimensional discrete uncoupled frictional contact problem. Three loading cases include (1) a normal force is constant and a tangential force varies, (2) normal and tangential forces both vary, but the loading and unloading curves are identical, and (3) normal and tangential forces both vary, but the loading and unloading curves are different. For a higher coefficient of friction, three loading cases show different characteristics. If a normal force is constant and a tangential force varies, there is always some slip, but dissipation tends asymptotically to zero at large coefficient of friction. If normal and tangential forces both vary, but the loading and unloading curves are identical, there is no slip and no dissipation above a critical coefficient of friction. If the loading and unloading curves are different, dissipation occurs for all values of the coefficient of friction, and we expect that the dissipation is asymptotic to the relaxation damping value as the coefficient of friction approaches infinity. For lowering coefficient of friction, the three loading cases show similar behavior. Dissipation increases and reaches a maximum just before a state where gross slip is possible.