Simplifying Data Processing in AFM Nanoindentation Experiments on Thin Samples

When testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, data processing is typically based on equations derived from Hertzian mechanics. To account for the finite thickness of the samples, precise extensions of Hertzian equations have been developed for b...

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Main Authors: Stylianos Vasileios Kontomaris, Anna Malamou, Andreas Stylianou
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Eng
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Online Access:https://www.mdpi.com/2673-4117/6/2/32
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author Stylianos Vasileios Kontomaris
Anna Malamou
Andreas Stylianou
author_facet Stylianos Vasileios Kontomaris
Anna Malamou
Andreas Stylianou
author_sort Stylianos Vasileios Kontomaris
collection DOAJ
description When testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, data processing is typically based on equations derived from Hertzian mechanics. To account for the finite thickness of the samples, precise extensions of Hertzian equations have been developed for both conical and parabolic indenters. However, these equations are often avoided due to the complexity of the fitting process. In this paper, the determination of Young’s modulus is significantly simplified when testing soft, thin samples on rigid substrates. Using the weighted mean value theorem for integrals, an ‘average value’ of the correction function (symbolized as g(c)) due to the substrate effect for a specific indentation depth is derived. These values (g(c)) are presented for both conical and parabolic indentations in the domain 0 < r/H ≤ 1, where r is the contact radius between the indenter and the sample, and H is the sample’s thickness. The major advantage of this approach is that it can be applied using only the area under the force–indentation curve (which represents the work performed by the indenter) and the correction factor g(c). Examples from indentation experiments on fibroblasts, along with simulated data processed using the method presented in this paper, are also included.
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spelling doaj-art-3310cadf0f4a4e33a8b38e9683f6b37a2025-08-20T03:12:08ZengMDPI AGEng2673-41172025-02-01623210.3390/eng6020032Simplifying Data Processing in AFM Nanoindentation Experiments on Thin SamplesStylianos Vasileios Kontomaris0Anna Malamou1Andreas Stylianou2Cancer Mechanobiology and Applied Biophysics Group, School of Sciences, European University Cyprus, 2404 Nicosia, CyprusSchool of Electrical and Computer Engineering, National Technical University of Athens, 15773 Athens, GreeceCancer Mechanobiology and Applied Biophysics Group, School of Sciences, European University Cyprus, 2404 Nicosia, CyprusWhen testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, data processing is typically based on equations derived from Hertzian mechanics. To account for the finite thickness of the samples, precise extensions of Hertzian equations have been developed for both conical and parabolic indenters. However, these equations are often avoided due to the complexity of the fitting process. In this paper, the determination of Young’s modulus is significantly simplified when testing soft, thin samples on rigid substrates. Using the weighted mean value theorem for integrals, an ‘average value’ of the correction function (symbolized as g(c)) due to the substrate effect for a specific indentation depth is derived. These values (g(c)) are presented for both conical and parabolic indentations in the domain 0 < r/H ≤ 1, where r is the contact radius between the indenter and the sample, and H is the sample’s thickness. The major advantage of this approach is that it can be applied using only the area under the force–indentation curve (which represents the work performed by the indenter) and the correction factor g(c). Examples from indentation experiments on fibroblasts, along with simulated data processed using the method presented in this paper, are also included.https://www.mdpi.com/2673-4117/6/2/32simplifying fitting processadherent samplesBuckle’s rulecellsAFM in medicine
spellingShingle Stylianos Vasileios Kontomaris
Anna Malamou
Andreas Stylianou
Simplifying Data Processing in AFM Nanoindentation Experiments on Thin Samples
Eng
simplifying fitting process
adherent samples
Buckle’s rule
cells
AFM in medicine
title Simplifying Data Processing in AFM Nanoindentation Experiments on Thin Samples
title_full Simplifying Data Processing in AFM Nanoindentation Experiments on Thin Samples
title_fullStr Simplifying Data Processing in AFM Nanoindentation Experiments on Thin Samples
title_full_unstemmed Simplifying Data Processing in AFM Nanoindentation Experiments on Thin Samples
title_short Simplifying Data Processing in AFM Nanoindentation Experiments on Thin Samples
title_sort simplifying data processing in afm nanoindentation experiments on thin samples
topic simplifying fitting process
adherent samples
Buckle’s rule
cells
AFM in medicine
url https://www.mdpi.com/2673-4117/6/2/32
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AT annamalamou simplifyingdataprocessinginafmnanoindentationexperimentsonthinsamples
AT andreasstylianou simplifyingdataprocessinginafmnanoindentationexperimentsonthinsamples