Journal - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Abstract :

Using an acoustic model for the full elastic problem, the earlytimes of the two-dimensional impact of a disc on a rigid plane,or impact between two identical discs, are analysed. We examinesome aspects of wave propagation during the impact process andspecify stress distributions near the impact region. Unlikethe impact of two spheres for which the quasi-static local contactapproach of Hertz is well adapted, a complete dynamical approachis necessary for the dynamic contact of two discs. At shorttimes after impact, we show the existence of supersonic effectsand we determine the shape of the corresponding stress wavesthat travel from the impact region through the unstressed body.During the supersonic phase, the contact region grows fasterthan the speed of sound and the surface outside the contactregion is undisturbed. We then solve the transition from supersonicto subsonic regimes and determine the stress distribution nearthe impact region. Finally, we discuss some physical implicationsof these results.