Dynamic indentation of an elastic half-plane by a rigid wedge: Frictional and tangential-displacement effects

Abstract

A dynamical contact problem is studied in this paper. It involves an elastic half-plane which is indented by a rigid wedge-shaped body. In an effort to depart from the classical formulation of this problem, we consider frictional and tangential-displacement effects. More specifically, it is assumed that Coulomb friction develops between the contacting bodies and also that the tangential surface displacements are not negligible and should thus be coupled with the normal surface displacements in imposing the contact-zone boundary conditions. Certainly, the foregoing considerations model the dynamic indentation of an elastic half-plane in a more realistic way than the usual frictionless and uncoupled formulation. The contact region is assumed to extend at a constant sub-Rayleigh speed (this situation can be achieved by conveniently specifying the indentor kinetics), whereas, due to symmetry, friction may act in opposing directions on opposite sides of the indentor. The study exploits the problem's self-similarity by utilizing homogeneous-function techniques along with the Riemann-Hilbert problem analysis. As the present exact analysis shows, both the sign reversal of the tangential traction and the coupling of the displacement components along the contact length strongly influence the contact-stress behavior at the wedge-apex station. In particular, friction tends to create a power-type singularity at the changeover point of boundary conditions (due to symmetry, this point here is the point where the wedge apex makes contact with the half-plane surface), whereas the tangential-displacement effect tends to eliminate singular behavior there. Representative numerical results are given for the normal stress and tangential displacement along the contact zone, and the relation between the contact-zone expansion velocity and the indentor velocity.