Finite Element Analysis of Contact Radius and Young’s Modulus Bias in Polymer Indentation

Contact mechanics models are often inaccurate, due to (i) unknown contact radius, (ii) mechanical models not parameterizing it, (iii) in some models it is neither assumed meaningfully nor determined, and (iv) uncertain probe radius arising from manufacturer-specified nominal values and manufacturing tolerances. In this paper, an FEA model was used to quantify the evolution of the contact radius during indentation for two probe geometries: a pyramidal indenter (TRIANG2 nominal apex radius 2 nm) and a flat-ended punch (FLAT4000; nominal punch radius 4000 nm) on poly (vinyl chloride) (PVC), for which Young’s modulus (Eref) was obtained by a standard mechanical tensile method. The effective contact radius, Reff, determined from FEA, was subsequently used in a Hertz-based force–indentation parametrization. Uncertainty in the probe apex radius due to manufacturer tolerances was addressed by SEM measurement of the conical tip, enabling assessment of its impact on the modulus estimated from AFM indentation. Based on these results, we propose a practical, geometry-aware analysis methodology that is transferable across probe geometries. The effective contact radius, Reff, is first established using a well-characterized reference material and subsequently applied to a mechanical model to extract Young’s modulus. In this approach, the Hertz-based parametrization is used as a consistent mathematical framework, while the effective contact radius accounts for probe-dependent contact evolution.