Tangential-displacement effects in the wedge indentation of an elastic half-space – an integral-equation approach

The idea of considering tangential-displacement effects in a classical elastostatic contact problem is explored in this paper. The problem involves the static frictionless indentation of a linearly elastic half-plane by a rigid wedge, and its present formulation implies 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. L.M. Brock introduced this idea some years ago in treating self-similar elastodynamic contact problems, and his studies indicated that such a formulation strongly influences the contact-stress behavior at half-plane points making contact with geometrical discontinuities of the indentor. The present work again demonstrates, by studying an even more classical problem, that the aforementioned considerations eliminate contact-stress singularities and therefore yield a more natural solution behavior. In particular, the familiar wedge-apex logarithmic stress-singularity encountered within the standard formulation of the problem (i.e. by avoiding the tangential displacement in the contact boundary condition) disappears within the proposed formulation. The contact stress beneath the wedge apex takes now a finite value depending on the wedge inclination angle and the material constants. By utilizing pertinent integral relations for the displacement/stress field in the half-plane, an unusual mixed boundary-value problem results whose solution is obtained through integral equations.