This paper presents the analysis of a layered elastic half space under the action of axisymmetric surface loading and the influence of the surface energy effects. The boundary value problems for the bulk and the surface are formulated based on classical linear elasticity and a complete Gurtin-Murdoch constitutive relation. An analytical technique using Love’s representation and the Hankel integral transform is employed to derive an integral-form solution for both displacement and stress fields. An efficient numerical quadrature is then applied to accurately evaluate all involved integrals. Selected numerical results are presented to portray the influence of various parameters on elastic fields. Numerical results indicate that the surface stress displays a significant influence on both displacement and stress fields. It is also found that the layered half space becomes stiffer with the presence of surface stresses. In addition, unlike the classical elasticity solution, size-dependent behavior of elastic fields is noted. The present analytical solutions provide fundamental understanding of the influence of surface energy on layered elastic materials. It can also be used as a benchmark solution for the development of numerical techniques such as FEM and BEM, for analysis of more complex problems involving a layered medium under the influence of surface energy effects.

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This paper presents the analysis of an axisymmetric frictionless rigid punch on a layered elastic medium with the consideration of surface energy effects by adopting Gurtin-Murdoch continuum theory of surface elasticity. The indentation problem is formulated as a mixed-boundary value problem with the displacement boundary condition being imposed at the contact area. The unknown contact pressure under the indenter is then determined by employing a discretization technique with use of the displacement Green’s functions. The required Green’s functions are expressed in the form of the Hankel integral transform. The accuracy of the proposed solution scheme is verified by comparing with existing solutions. Selected numerical results on displacement and stress profiles in a layered elastic half-space are presented to demonstrate the influence of various parameters on elastic fields. It is found that the layered medium becomes stiffer and shows size-dependent behavior due to the presence of surface stresses.