Torsion of a circular punch attached to an elastic half-space with a coating with periodically depth-varying elastic properties

Torsion of a non-deformable circular punch attached to an elastic half-space with functionally graded or multilayered coating is considered. The coating is represented by a set of alternating soft and hard (in terms of shear modulus values) layers. The boundaries of the layers can be sharp (piecewise-constant variation of the shear modulus) or smooth (continuously inhomogeneous or functionally graded coatings). An approximate analytical solution of high accuracy applicable for any value of coating thickness is constructed. The influence of number of layers and type of the boundaries between them on the kernel transform of the integral equation and on the contact stresses under the punch is investigated. It is shown that for certain parameter values of the problem substantial differences between the results for the continuous and piecewise-constant variation of the shear modulus with depth are obtained.