Couple stress effects in a thin film bonded to a half-space

This study investigates the contact mechanics of a thin film laying on an elastic substrate within the context of couple-stress elasticity. It aims to introduce the effects of material internal length scale, which has proven an effective way of modeling structures at micro to nano-scales, allowing to capture their size dependent behavior. Specifically, stress analysis for a thin film bonded to a couple stress elastic half-space is considered under plane strain loading conditions by assuming that both shear stress and couple tractions are exchanged between the thin film and the substrate. The problem is converted to a singular integral equation, which is solved by expanding the shear stress tractions as a Chebyshev series. The results show that the introduction of couple tractions decreases the shear stress tractions and the axial load in the thin film. When the characteristic length is sufficiently small, but still finite, the results for classical elastic behavior are approached.