Effects of Couple Tractions on Contact Problems at the Microscale

In this study, the problem of a thin film loaded at both ends and in contact with a microstructured substrate modelled by the couple stress theory of elasticity is investigated. To appropriately define the microstructural contact conditions the contribution of couple tractions is considered. By using the Green's functions for a tangential point force and a couple acting on the surface of a couple stress elastic half-plane, the extended boundary conditions, which enforce compatibility between the displacement and rotations along the contact region, provide two singular integral equations. One of them yields an explicit relation for couple tractions in terms of the interfacial shear stress. By assuming a series of Chebyshev polynomials for the distributions of shear stress along the contact region and using a collocation method, the remaining integral equation is reduced to an algebraic system for the Chebyshev series coefficients. Finally, the axial load in the thin film is computed while varying the characteristic length of the substrate, revealing significant deviations from the classical elastic solution.