Is there anyone knows how to derivate the equations in Hertz's paper ? Any detailed lessons, or lectures? I want to have a deeper understanding of Hertz contact mechanic model used in fiting force curve obtained from AFM. Thanks in advance.
I recommend reading Valentin Popov here - especially the book
Book Contact Mechanics and Friction: Physical Principles and Applications
Chapter 5 ("Rigorous Treatment of Contact Problems -Hertzian Contact") should already help you, I think.
Dear Ronny:
thanks a lot for your recommandation! i will check it out.
Best Regards!
The thing is that nowadays almost nobody uses Hertz's formalism anymore, which is based on the solution of an electrostatic equivalent problem with the means of potential theory.
There are several easier ways to obtain Hertz's solution, especially for the axisymmetric case.
For the general (elliptical) Hertzian contact problem, the most principled solution is via field point integration of the pressure distribution, as discussed in detail in the books on Contact Mechanics by Johnson (1985) and Barber (2018).
Dear Emanuel Willert, thanks for your answer. I checked the two books you mentioned. I prefer the Johnson (1985) with detailed math content related to hertz model.
Another book where the derivation is presented concisely is Landau & Lifshitz, Theoretical Physics, Vol. VII (Theory of Elasticity), chapter 9.
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