Dynamic frictional indentation of an elastic half-plane by a rigid punch

Abstract

Dynamic rigid indentation of a linearly elastic half-plane in the presence of Coulomb friction is studied in this paper. A rigid punch, which is either wedge- or parabolic-shaped, is rapidly driven into the deformable body so that stress waves are generated. The contact region is assumed to extend at a constant sub-Rayleigh speed (this situation can be achieved by conveniently specifying the kinetic and geometric characteristics of indentor), whereas, due to symmetry, friction acts in opposing directions on opposite sides of the indentor. As the present exact analysis shows, this sign reversal of the tangential traction along the half-plane surface creates an extra stress-singularity at the changeover point of the boundary conditions (due to symmetry, this point here coincides with the point where the indentor apex makes contact with the half-plane surface). The study exploits the problem's self-similarity by utilizing homogeneous-function techniques previously used by L.M. Brock, along with the Riemann-Hilbert problem analysis. Representative numerical results are given for the wedge indentation case.