An adhesive contact problem for an incompressible non-homogeneous elastic halfspace

In this paper, we examine the axisymmetric adhesive contact problem for a rigid circular plate and an incompressible elastic halfspace where the linear elastic shear modulus varies exponentially with depth. The analytical solution of the mixed boundary value problem entails a set of coupled integral equations that cannot be solved easily by conventional integral transform techniques proposed in the literature. In this paper, we adopt a computational scheme where the contact normal and contact shear stress distributions are approximated by their discretized equivalents. The consideration of compatibility of deformations due to the indentation by a rigid indenter in adhesive contact gives a set of algebraic equations that yield the discretized equivalents of the contacts stresses and the axial stiffness of the medium.