On the smoothness of the surface deformation profile due to the indentation of an elastic half-space

Although the surface deformation concept has been used in the nanoindentation study, there is a lack of investigation on the smoothness of the surface deformation profile. We find that the surface deformation profile is continuous while its first order derivative is continuous only for incomplete and critical complete contact situations. The presented result may be used to make more realistic assumptions on the surface deformation in the nanoindentation modeling.