i do not believe that convergence tolerance controls this
i also do not believe that the result will 100% match your stress strain curve
what is the reason for it needing to be exact?
and i'm assuming that mesh has no influence on the results?
No, you are right, it don't need to be exact, after all it's FEA, an approximation.
My only curiosity is why it always stays a little low on strain for each stress level compared to the input on the SS curve.
I thought this was something that you could tweak in the settings, but perhaps it isn't.
Mesh size isn't affecting this, not in the trials I did anyway, and I tried a couple of materials with similar result.
create a similar case with a cantilever beam and post it