Could you plot a least square error fit for x^1.5 and see how much the difference is? Also from the first image it looks like the deformation is large and thus not consistent with the small strain assumption. You may want to reduce your displacement to a very small value and then check the trend. Also, If you are comparing your simulation with a analytical solution based on linear elastic assumption, it would be better to switch large deflection off. I hope you are using a very fine mesh near the contact. The sphere of influence would be best suited for this problem.
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