Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Nanoindentation is employed to characterize the mechanical properties at the nanoscale. This paper considers the mechanical response of a nanoscale elastic layer on an elastic substrate that is indented by an adhesively bonded flat-ended rigid cylindrical punch. The complete Gurtin–Murdoch continuum model is employed to capture the size effects. The contact problem is analyzed by relating displacements of the contact region to contact stresses by a flexibility equation system, which is developed by discretizing the contact region into annular elements. The flexibility equation involves displacement influence functions corresponding to axisymmetric normal and radial surface ring loads applied on the layer-substrate system. The displacement influence functions are derived by using the Hankel integral transforms. Convergence and accuracy of the proposed solution scheme are verified by comparing with limiting cases such as the classical elasticity solution. Selected numerical results indicate that the substrate becomes stiffer and the elastic field is size-dependent due to the surface energy effects.