An extension of the general nanoindentation equation regarding cylindrical-shaped samples and a simplified model for the contact ellipse determination

The mechanical properties of biomaterials and biological samples at the nanoscale can be determined using the AFM nanoindentation method. Typical biological samples are the fibrous proteins which can be modelled as cylindrical-shaped samples. However, the nanoindentation method for such samples is a challenging procedure due to the fact that the projected contact area between a spherical indenter and the sample is elliptical and as a result advanced mathematical analysis is required. Several approximations are commonly used to avoid the complexity, which, however, result in significant errors in the analysis. The purpose of this paper is to present a new simplified technique which extends the applicability of the general nanoindentation equation for cases that concern cylindrical-shaped samples. The proposed analysis results in the accurate calculation of the projected contact area and can be generally applied when biological samples and biomaterials with cylindrical symmetry are being tested using spherical indenters.