5. Tangential Contact

The fundamental property that allows the reduction of three-dimensional contacts to those in one dimension is the proportionality of the incremental stiffness to the diameter of the contact area. This property is exhibited by both normal and tangential contacts. The idea behind dimensionality reduction can, therefore, be directly transferred to tangential contacts. More accurately, the transferability of the method of dimensionality reduction to tangential contacts follows from the ideas and results from Cattaneo, Mindlin, Jäger, and Ciavarella about the close relationship between normal and tangential contacts. In this chapter, we will show how tangential contacts exhibiting Coulomb friction with arbitrarily axially-symmetric profiles can be exactly mapped onto a properly defined one-dimensional elastic foundation.