The axisymmetric contact problem of the indentation of a conical punch into a half-space with a coating inhomogeneous in depth

A semi-analytical solution of the contact problem of the indentation of a conical punch into a half-space with a coating inhomogeneous in depth is obtained. Young's modulus and Poisson's ratio in the coating very arbitrarily with depth. The solution is asymptotically exact for large and small values of the geometrical parameter of the problem (the ratio of the coating thickness to the radius of the contact area). Numerical values of the contact stresses are constructed using the example of a linear variation of Young's modulus in the coating.