“…Engineering methods for solving contact problems on the basis of simplifying hypotheses, for example, the representation of a layered body as a topocomposite-constructions with special mechanical properties, depending on the mechanical properties of the base and coating materials, the thickness of the coating, should be included in a separate group. In [9,10], it was proposed to use the Hertz theory for this purpose. On the basis of reliable results for the extreme thickness values of the coating, an expression is obtained for the dimensionless elastic geometric parameter Φ connecting the displacement of the surface of the topocomposite with the displacement of the surface of a homogeneous half-space from the base material.…”