Rigid frictionless indentation on elastic half space with influence of surface stresses

This paper proposes an application of continuum-based concepts in the analysis of an axisymmetric rigid frictionless indentor acting on an isotropic, linearly elastic half-space accounted for surface energy effects. The influence of surface stresses is considered by employing a complete Gurtin–Murdoch continuum model for surface elasticity. With use of standard Love’s representation and Hankel integral transform, such boundary value problem is reduced to a set of dual integral equations that can be further transformed into an equivalent Fredholm integral equation of the second kind. Selected numerical procedures based on the solution discretization and standard collocation technique are then implemented to construct its solution numerically. Obtained numerical results for elastic fields within the bulk are shown and compared for indentors of different profiles and contact radii at various depths. It is found that the influence of surface free energy on bulk stresses and displacements and the size-dependency of solutions become more apparent in a region very near the free surface. The significant contribution of the residual surface tension on predicted responses is obviously observed in comparison with existing results. The proposed mathematical model not only offers an alternative for specifically studying both mechanical properties and elastic fields for indentors of arbitrary axisymmetric profiles but also provides, in general, a crucial basis for further investigations in the area of nano-mechanics.