The elastic field for an upright or tilted sliding circular flat punch on a transversely isotropic half space (Q1317508)

Most of the previous works have dealt with calculating quantities on the surface only and have considered only isotropic materials. Very few investigators have evaluated closed form expressions for the elastic field. This paper gives closed form expressions for the displacement and stress fields in a transversely isotropic half-space 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 the direction of shear traction. It is shown that the interaction between the surface stresses vanishes for a particular value of the elastic constants, and it is shown in some instances that the tangential displacements align with the shear traction thus yielding an exact solution. The author proves also 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 loading at infinity. Some numerical results are given to illustrate the effects of transverse isotropy and shear loading on the internal stress fields.