Driving forces in moving-contact problems of dynamic elasticity: Indentation, wedging and free sliding

The steady-state solution for an elastic half-plane under a moving frictionless smooth indenter of arbitrary shape is derived based on the corresponding transient problem and on a condition concerning energy fluxes. Resulting stresses and displacements are found explicitly starting from their expressions in terms of a single analytical function. This solution incorporates all speed ranges, including the super-Rayleigh subsonic and intersonic speed regimes, which received no final description to date. Next, under a similar formulation the wedging of an elastic plane is considered for a finite wedge moving at a distance from the crack tip. Finally, we solve the problem for such a wedge moving along the interface of two elastic half-planes compressed together. Considering these problems we determine the driving forces caused by the main underlying factors: the stress field singular points on the contact area (super-Rayleigh subsonic speed regime), the wave radiation (intersonic and supersonic regimes) and the fracture resistance (wedging problem). In addition to the sub-Rayleigh speed regime, where the sliding contact itself gives no contribution to the driving forces, there exists a sharp decrease in the resistance in the vicinity of the longitudinal wave speed with zero limit at this speed.