Torsion of elastic half-space with multilayered coating of periodic structure

An axisymmetric problem of the elasticity theory on torsion of an elastic half-space with inhomogeneous in depth coating of periodic structure by a non-deformable circular punch is considered. The coating is represented by a set of alternating soft and hard layers. The boundaries of the layers can be clear (piecewise-constant variation of the shear modulus) or smooth (continuously inhomogeneous or functionally-graded coatings). The approximate analytical solution to the problem of high accuracy is constructed which is effective for any coating thickness. The effect of the number of layers, and of the coating inhomogeneity type on the kernel transform of the integral equation and on the contact stresses distribution under the punch is investigated. It is shown that with certain values of the problem parameters, the substantial difference between the results for the continuous and piecewise constant type of the variation of the shear modulus in depth is obtained.