Thickness-corrected model for nanoindentation of thin films with conical indenters

Abstract

Nanoindentation of soft materials is a growing research field, demanding sophisticated models to extract accurate information from these materials. In this work we investigate the nanoindentation of thin soft films by sharp conical indenters using Finite Elements Modeling. Based on the work of Dimitriadis et al. [Biophys. J. 82, 2798 (2002)], we propose that load-displacement (F × δ) curves for conical indenters can be described by F = FHertz(δ)g[χ(δ,h)], where FHertz(δ) is the regular Hertz model, and g[χ(δ,h)] is a correction function that includes finite thickness effects. To test the applicability of the model, we analyze the elastic modulus of fibroblast cells as measured by Atomic Force Microscopy. The elastic modulus obtained with Hertz model is overestimated by 50% (when compared to our thickness-corrected model) in the thickest parts of the cell (3.67 μm), and by approximately 128% in the lamellipodia region (0.45 μm), illustrating the importance of the sample thickness for the evaluation of the mechanical properties.