Tangential contact of elastically similar bodies

This chapter is devoted to the so-called local tangential contact of two elastic bodies, which meet at a single point in the load-free state and whose stress-displacement states in the deformed configuration can be approximated by those of the corresponding elastic half-spaces when subjected to symmetric normal pressures and tangential tractions. It is assumed that the elastic constants of the contacting bodies satisfy a certain relationship, so that there is no coupling between normal and tangential displacements. This, in particular, means that the normal loading does not generate any tangential tractions at the contact interface, and that any subsequent tangential loading does not alter the established normal contact pressure pattern. Moreover, it is assumed that Coulomb’s law of sliding friction governs the evolution of the stick and slip zones under shift and torsion. In the case of a Hertz-type contact geometry (a gap between the contacting surfaces in the undeformed state is approximated by an elliptic paraboloid), the theory of local tangential contact of two isotropic bodies was independently developed by Cattaneo [3] and Mindlin [16]. Under the assumption of axial symmetry, the Cattaneo–Mindlin theory was generalized by Jäger [12] for an arbitrary gap profile. Here we extend Jäger’s results to the transversely isotropic case.