The data processing regarding AFM nanoindentation experiments on biological samples relies on the basic contact mechanics models like the Hertz model and the Oliver & Pharr analysis. Despite the fact that the two aforementioned techniques are assumed to provide equivalent results since they are based on the same underlying theory of contact mechanics, significant differences regarding the Young's modulus calculation even on the same tested sample have been presented in the literature. The differences can be even greater than 30% depending on the used model. In addition, when the Oliver & Pharr analysis is used, a systematic greater Young's modulus value is always calculated compared to the Hertzian analysis. In this paper, the two techniques are briefly described and two possible reasons that accurately explain the observed differences in the calculated value of the Young's modulus are presented.

Assume a rigid sphere that is slightly pushed towards an elastic half space. The applied force on the half space can be easily calculated using the basic theoretical tools provided by the Hertzian contact mechanics theory. It should be noted that the aforementioned analysis is valid under the condition that the deformation depth is significantly smaller compared to the sphere’s radius (h ≪ R). So, a significant question arises; what if the sphere is pushed deeper in the elastic half space (e.g. h > R)? In this paper, the aforementioned question is answered and a relative discussion regarding the application of the results is presented.

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