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	Hertz Contact Mechanics - Panel
	Hertz Contact Mechanics - Panel

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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:

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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>

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

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Furthermore, we can derive the following formula for the normal stresses σ_z and σ_r = σ_θ along the z-axis.

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Here we note that the principal normal stresses σ₁ = σ₂ = σ_r = σ_θ since the out-of-plane shear stresses, τ_rz = τ_θz = 0 and σ₃ = σ_z. And we can deduce that τ_max = |τ₁|=|τ₂|=|(σ₁-σ₂) / 2|. The effective stress (using the Von-Mises criterion) along the y-axis can be computed as the following:

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