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• Hertz Contact Mechanics - Verification & Validation

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# Verification and Validation

This section contains a few formulae, which made the listed assumptions, found in the Pre-Analysis & Start-Up page.

The analytical formula for computing the radius of contact zone (a) is given as follows:

The following command for the computation of the contact area can be downloaded here.

• This command was generously provided by Mr. Sean Harvey. (Lead Technical Services Engineer at Ansys Inc.)

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<iframe width="600" height="450" src="//www.youtube.com/embed/0ZI-QVUEJgk?rel=0" frameborder="0" allowfullscreen></iframe>

Using this value of contact radius, we can also compute the normal pressured induced at the contact zone.  Theoretically, the maximum pressure (pmax) is induced along the y-axis, as expected, and is given by the following formula:

Furthermore, we can derive the following formula for the normal stresses σz and σr = σθ along the z-axis.

Here we note that the principal normal stresses σ1 = σ2 = σr = σθ since the out-of-plane shear stresses, τrz = τθz = 0 and σ3 = σz.  And we can deduce that τmax = |τ1|=|τ2|=|(σ12) / 2|.  The effective stress (using the Von-Mises criterion) along the y-axis can be computed as the following:

Lastly, we also confirm that the applied load at the top vertex of the sphere matches our numerical contact pressure, integrated along the interface.