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A Discussion Regarding the Application of the Hertz Contact Theory on Biological Samples in AFM Nanoindentation Experiments

Author(s):

S. V. Kontomaris*, A. Stylianou, K. S. Nikita and A. Malamou   Pages 1 - 7 ( 7 )

Abstract:


Atomic Force Microscopy (AFM) Nanoindentation procedure regarding biological samples poses significant challenges with respect to the accuracy of the provided results. These challenges are related to the inhomogeneity of biological samples, various uncertainties in experimental methods and certain approximations regarding the theoretical analysis. The most commonly used theoretical model for data processing at the linear elastic regime regarding biological samples is the Hertz model. This paper focuses on the investigation of the resulting errors of the basic equation of the Hertz theory that depends on the ratio, indentation depth/indenter’s radius regarding the Young’s modulus calculation. Several examples in the literature that do not take into account the value of the ratio indentation depth/indenter’s radius are reported and the related errors are presented and discussed. In addition, an extended new equation is derived which takes into account the influence of the aforementioned ratio on the calculation of the Young’s modulus and can be easily used for calculations. Moreover, a rational explanation, regarding the extended differences of the Young’s modulus calculations using the same experimental results when these are processed using the Hertz model and the Oliver & Pharr analysis (which is the general model that applies for any axisymmetric indenter) is provided. In conclusion, the derived equation is further combined with equations which take into account the shape of the sample in order to provide a complete and reliable theoretical tool which can be generally applied in order to reduce the errors produced by the current methodology.

Keywords:

Mechanical properties, hertz model, biological samples, Atomic Force Microscopy (AFM) nanoindentation, indentation values.

Affiliation:

Mobile Radio Communications Laboratory, School of Electrical and Computer Engineering, National Technical University of Athens, Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, Faculty of Engineering, University of Cyprus, Mobile Radio Communications Laboratory, School of Electrical and Computer Engineering, National Technical University of Athens, Radar Systems and Remote Sensing Lab of School of Electrical & Computer Engineering of National Technical University of Athens



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