The elastic field for an upright or tilted sliding circular flat punch on a transversely isotropic half space

This paper gives closed form expressions for the displacement and stress fields in a transversely isotropic half space when the surface is loaded in shear by a sliding circular flat punch in either an upright or inclined position. The shear traction on the surface is taken as a friction coefficient multiplied by the frictionless contact pressure. The solution derived here for shear loading is generally approximate since the interaction between the normal and shear loading is ignored and the relative displacements do not necessarily align to the direction of shear traction. However, it is shown that the interaction between the surface stresses vanishes for a particular value of the elastic constants and it is also shown that in some instances the tangential displacments do align with the shear traction thus yielding an exact solution. It is furthermore shown that the solution for a sliding flat upright indenter is an exact solution to the problem of a circular external crack in an infinite transversely isotropic body subjected to uniform tangential displacement loading at infinity. Numerical results for the subsurface stress fields are given to illustrate the effects of sliding and transverse isotropy.