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 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.