Is the Hertz model correct?

Submitted by qq935074410 on Thu, 04/30/2020 - 03:30

Dear all,

I was looking at the documentation of the hertz model and have a question about the following equation.
K_n = 4/3 Y*(R*delta)^(1/2)

I derived this equation from the hertz model and find the equation should be
K_n = 4/3 Y*R*^(1/2)delta^(3/2)

This result is also given by the wikipedia and some other papers.

Could anyone tell me which one is the correct one? This may have a great influence when the large cohesion is added.

Thanks,
Brian

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Daniel Queteschiner | Thu, 04/30/2020 - 09:34

You are mixing up the stiffness coefficient k_n = 4/3 Y*(R*delta)^(1/2) and the force F_n = k_n delta = 4/3 Y*R*^(1/2) delta^(3/2).
The definition of the stiffness coefficient and the expression for the force may vary (resulting in the same final equation, though),
e.g. sometimes k_n is defined as k_n = 4/3 Y*(R*)^(1/2) and the force is then given as F_n = k_n delta^(3/2) = 4/3 Y*R*^(1/2) delta^(3/2).