Partial slip contact between a rigid punch with an arbitrary tip-shape and an elastic graded solid with a finite thickness

In contrast to the case of a graded half-space, a nonlinear plane strain partial slip model between a rigid punch with an arbitrary tip-shape and a finite graded solid is investigated. The modulus of the finite graded solid varies according to an exponential function in the thickness direction. Fourier integral transform method is adopted in order to reduce the current nonlinear problem to a set of singular integral equations. Based on the Goodman's approximation, the contact problem is simplified. An iterative method is used to determine the size of the contact zone, the interface stress singularity, as well as the distributions of the normal and tangential stresses. The effects of different parameters on the contact behavior, such as the ratio of shear modulus, the friction coefficient and the thickness of the graded solid, are analyzed. The results exhibit significant differences between the model of a half-space and the present one of a finite solid, which highlights the practicability of the present model for practical engineering applications and the design of novel graded materials.