Supersonic and subsonic stages of dynamic contact between bodies

Using an acoustic model for the full elastic problem, the early times of the two-dimensional impact of a disc on a rigid plane, or impact between two identical discs, are analysed. We examine some aspects of wave propagation during the impact process and specify stress distributions near the impact region. Unlike the impact of two spheres for which the quasi-static local contact approach of Hertz is well adapted, a complete dynamical approach is necessary for the dynamic contact of two discs. At short times after impact, we show the existence of supersonic effects and we determine the shape of the corresponding stress waves that travel from the impact region through the unstressed body. During the supersonic phase, the contact region grows faster than the speed of sound and the surface outside the contact region is undisturbed. We then solve the transition from supersonic to subsonic regimes and determine the stress distribution near the impact region. Finally, we discuss some physical implications of these results.