Abstract
This study discusses the application of a hybrid experimental-numerical approach to analyze nano-indentation curves of a biological membrane acquired with an Atomic Force Microscope. The proposed procedure combines experimental measurements, FEM analysis and numerical optimization and is completely general. Variations of estimated Young modulus of the membrane are determined when attributing different constitutive laws to the sample and in the case of progressive blunting of the AFM tip during the measurement. Since traditional analysis of Atomic Force Microscope indentation curves relies on an inappropriate application of the classical Hertz theory, a comparison between the hybrid approach and the Hertzian model in the determination of the elastic properties of the sample is presented. In particular, it is found that large errors occur in the derivation of the Young modulus when the Hertzian model is used for the analyis of experimental data.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hertz H. On the contact of elastic solids. Journal für die Reine und Angewandte Mathematik, 92, 156–171, 1881.
Sneddon I.N. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. International Journal of Engineering Science, 3, 47–57, 1965.
Costa K.D., Yin F.C.P. Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy. Journal of Biomechanical Engineering, 121, 462–471, 1999.
Costa K.D., Sim A.J., Yin F.C.P. Non-Hertzian approach to analyzing mechanical properties of endothelial cells probed by atomic force microscopy. Journal of Biomechanical Engineering 128, 176–184, 2006.
Lin D.C., Shreiber D.I., Dimitriadis E.K., Horkay F. Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models. Biomechanics and Modeling in Mechanobiology, 8, 345–358, 2009.
Kang I., Panneerselvam D., Panoskaltsis V.P., Eppel S.J., Marchant R.E., Doerschuk C.M. Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-α. Biophysical J. 94, 3273–3285, 2008.
Dassault Systèmes, 2007. ABAQUS Version 6.7. Theory and User’s Manual. www.simulia.com
Mooney M. A theory of large elastic deformation. Journal of Applied Physics 11, 582–592, 1940.
Rivlin R.S. Large elastic deformations of isotropic materials I. Fundamental concepts. Philosophical Transactions of the Royal Society of London, A240, 459–490, 1948.
Rivlin R.S. Large elastic deformations of isotropic materials IV. Further developments of the general theory. Philosophical Transactions of the Royal Society of London, A241, 379–397, 1948.
Treolar L.R.G. The Physics of Rubber Elasticity, 3rd Edn. Oxford University Press, Oxford (UK), 1975.
Arruda E.M., Boyce M.C. A three dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of Mechanics and Physics of Solids, 41, 389–412, 1993.
Bischoff J.E., Arruda E.M., Grosh K. Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model. Journal of Biomechanics, 33, 645–652, 2000.
Palmer J.S., Boyce M.C. Constitutive modeling of the stress–strain behavior of F-actin filament networks. Acta Biomaterialia, 4, 597–612, 2008.
Cosola E., Genovese K., Lamberti L., Pappalettere C. Mechanical characterization of biological membranes with moiré techniques and multi-point simulated annealing. EXPERIMENTAL MECHANICS 48, 465–478, 2008.
Cosola E., Genovese K., Lamberti L., Pappalettere C. Mechanical characterization of biological membranes with moiré techniques and multi-point simulated annealing. International Journal of Solids Structures, 45, 6074–6099, 2008.
Rao S.S. Engineering Optimization. John Wiley and Sons, New York (USA), 1996.
The MathWorks, MATLAB® Version 7.0. Austin (TX), 2006. http://www.mathworks.com
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Businees Media, LLC
About this paper
Cite this paper
Frassanito, M.C., Lamberti, L., Boccaccio, A., Pappalettere, C. (2011). Discussion on hybrid approach to determination of cell elastic properties. In: Proulx, T. (eds) Optical Measurements, Modeling, and Metrology, Volume 5. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0228-2_16
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0228-2_16
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0227-5
Online ISBN: 978-1-4614-0228-2
eBook Packages: EngineeringEngineering (R0)