Couple-stress analysis of sliding frictional contact in functionally graded elastic layers

This study investigates the two-dimensional sliding frictional contact problem of a functionally graded (FG) elastic layer pressed by a rigid cylindrical punch within the framework of couple-stress elasticity (CSE) to account for microstructural size effects. Coulomb friction conditions are assumed to prevail across the contact interface. The Poisson's ratio of the layer is kept constant, while its modulus of elasticity varies exponentially through the thickness. Utilizing integral transform techniques along with the boundary conditions, the contact problem is formulated as a singular integral equation of the second kind, where the contact stress function and the contact width are the primary unknowns. This singular integral equation is solved numerically via Jacobi polynomials and the Gauss{Jacobi integration formula, ensuring compliance with the equilibrium and consistency conditions. Finally, a comprehensive parametric analysis is conducted to evaluate the in uences of the characteristic material length, material inhomogeneity parameter, friction coefficient, punch radius, indentation load, and Poisson's ratio on both the contact stress distribution and the underlying in-plane stress fields.