A discussion regarding the approximation of cylindrical and spherical shaped samples as half spaces in AFM nanoindentation experiments

Abstract

A common assumption of nanoidentation experiments is to consider the sample as an elastic half space due to the simplicity of the analysis regarding the Young’s modulus calculation. However, in the nano—dimensions a sample cannot be considered as a half space and this approximation can lead to significant errors in the analysis. In this paper, the Atomic Force Microscopy (AFM) nanoindentation method on cylindrical and spherical shaped samples is discussed. The purpose of this paper is to investigate the errors that arise under the assumption that a cylindrical/spherical shaped sample is a half space and to provide a simplified methodology to reduce these errors. The new approach can be applied to AFM nanoindentation experiments on cylindrical or spherical biological samples (e.g. collagen fibers and cells).