Is it possible to use a model of a flat cylinder to fit force-distance curves from AFM?

What do you mean the Hertz model is "uncomfortable to use"? The use of a model should not be determined by its usage convenience.

Is this automated tool maybe helpful for your purposes?

http://www.biophysik.uni-bremen.de/start/radmacher-group/data-analysis/hertzfit/hertz-fit-downloads/

Sathya Prasad Mangalaramanan

It would not be out of place for me to share a few thoughts.

You have indicated that the force-displacement relationship is linear. However, there is a difference between metal indentation and polymer indentation. Metal indentation is due to ductility (well past E) and is permanent (like craters on moon!).

If you have linear F-d relationship, as in your case, that means after release of force, there is complete recovery without hysteresis (path independent). No permanent indentation marks, which makes our life a bit easier. Your indentor seems to have just kissed the polymer instead of taking a bite out of it! :-)

Hertz formula is quite approximate and I would discourage you from counting on it entirely.

I don't know how you derived your simple formula, but as a fan of thumb rules and approximation, if it makes sense, go for it.

I would additionally suggest the following (very simple steps):

Make a simple FEA model (2D, axisymmetric) with Young's modulus of the indentor (which I would assume as hemispherical - quarter circle in your FEA model) at least around 10000 times more than that of the polymer. Assume some low E value for the polymer.
Apply a prescribed displacement (in small steps) on the indentor
Fix the far edge of the polymer and calculate the Y reactions
Plot the sum of the Y reactions obtained from FEA versus the Y displacement that you have given on the indentor.
Play with the E value of the polymer until your Force-displacement curve from the indentation test matches with FEA results.
Make sure you have a fine mesh that conforms to contact progressively.

The FEA run would be quite fast and your estimated E value for polymer would be quite decent. Of course, we are assuming linear elastic material properties here, which for a polymer is a bit strange, unless we are talking about very small forces and displacements.

Only the very best to you my good friend!

Cheers!

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