Contact problem on torsion of transversely isotropic elastic half-space with inhomogeneous transversely isotropic coating by round die

An axisymmetric contact problem of the elasticity theory on the torsion of the transversely isotropic half-space with the inhomogeneous coating by the round die is considered. The problem solution is reduced to the integral equation solution using the integral transformations technique. The explicit expression of the kernel transform of the integral equation for the homogeneous transversely isotropic coating is constructed. The numerical construction scheme of the kernel transform in the case of the arbitrary law of variation of the coating depth shear modulus is suggested. The bilateral asymptotically exact approximate analytical problem solution is constructed using the kernel transform approximation by some special functions. A special case of variation of the shear moduli in the transversely isotropic coating that allows constructing an explicit closed problem solution is analyzed. The model problem on the biomaterial torsion is studied numerically. The coating is considered a cartilaginous tissue, and the substrate properties correspond to a cortical bone.