Reissner–Sagoci problem for functionally graded materials with arbitrary spatial variation of material properties

The paper considers the elastostatic problem related to the axisymmetric rotation of a rigid circular punch which is bonded to the surface of a functionally graded coating with arbitrarily varying shear modulus on a homogeneous half-space. The graded coating is modeled as a linear multi-layered medium. By the use of the transfer matrix method and Hankel transform technique, the problem is reduced to a singular integral equation. The stresses at the contacting surface are calculated by solving the equation numerically. The results show that the contact stresses are significantly affected by the gradient of the coating. This allows us to modify the distribution of the contact stress by adjusting the gradient of the coating. The results also provide us a possible way to measure the gradient of the coating using the non-destructive twisting test.