Non-axisymmetric frictionless indentation of a transversely isotropic elastic half-space

In this chapter, we consider non-axisymmetric frictionless unilateral contact and develop a generalization of the BASh relation, which accounts for non-circular contact areas. An important case of non-axisymmetric contact is characterized by a class of self-similar indenters, for which we outline a similarity analysis by Borodich (J Appl Math Mech 47:519–521, 1983 [9]), (Sov Appl Mech 26:631–636, 1990 [10]), where special attention is paid to pyramidal indenters.