It is extremely complex to do but it can be done using finite element analysis.
If the round surface is the same a one of the brinnell hardness testing ball scales, you can measure the impression and there are tables which tell you an average psi of the tensile strength. They don't tell you the actual though.
The problem is there is compressive force squeezing, and mixed tensile and friction forces from it trying so slide sideways. For flat faces this is well documented from "upset" calcs for forging. You can calc for various lubricants on the flat face, different temps etc.
You could calc an average psi, but what it is at each point is the tough part.
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