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Verification and Validation
This section contains a few formulae, which made the listed assumptions, found in the PreAnalysis & StartUp 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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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 yaxis, as expected, and is given by the following formula:
Furthermore, we can derive the following formula for the normal stresses σ_{z} and σ_{r} = σ_{θ} along the zaxis.
Here we note that the principal normal stresses σ_{1} = σ_{2} = σ_{r} = σ_{θ} since the outofplane shear stresses, τ_{rz} = τ_{θz} = 0 and σ_{3} = σ_{z}. And we can deduce that τ_{max} = τ_{1}=τ_{2}=(σ_{1}σ_{2}) / 2. The effective stress (using the VonMises criterion) along the yaxis 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.