Frictional Indentation of an Elastic Half-Space

In this chapter, we study the axisymmetric indentation problem for a transversely isotropic elastic half-space with finite friction. By treating the indentation problem incrementally, its general solution is reduced to that of the problem for a flat-ended cylindrical indenter with an unknown stick-slip radius. The solution to the latter problem in the transversely isotropic case is obtained via Turner’s equivalence principle Turner (Int J Solids Struct 16:409–419, 1980 [15]), from the analytical solution given by Spence (J Elast 5:297–319, 1975 [12]) in the case of isotropy. The generalization, due to Storåkers and Elaguine (J Mech Phys Solids 53:1422–1447, 2005 [14]), of the BASh relation for incremental indentation stiffness, and also accounting for the friction effects, is presented. The case of self-similar contact with friction is considered in more detail