Modeling axisymmetric frictional nanocontact of a finite-thickness elastic layer

In this paper, based on the C–Y surface energy elasticity theory, the axisymmetric frictional nanocontact problem of a finite-thickness elastic layer bonded to a rigid substrate is investigated. By introducing Love’s strain function and applying the Hankel integral transform, integral-form solutions for the stress and displacement fields of the finite-thickness elastic layer subjected to uniformly distributed pressure and friction are obtained. Numerical results demonstrate that surface effect, finite thickness, and friction jointly influence the nanocontact behavior of the elastic layer. Surface effect significantly suppresses the normal displacement and stress levels inside the contact area, leading to a pronounced hardening trend of the elastic layer. Decreasing the layer thickness enhances the constraint imposed by the rigid substrate, thereby reducing the surface normal displacement, which also stiffens the layer. Meanwhile, an increase in the friction coefficient also significantly suppresses the overall normal displacement. As a result, a generalized nanohardness is introduced to characterize the nanocontact property of the finite-thickness elastic layer; one can see that the nanohardness increases with increasing bulk surface energy density, decreasing layer thickness, and increasing friction coefficient. These results provide a basis for practical frictional nanocontact analysis and nanoindentation characterization of elastic layers.