Depending on the complexity of your model, you probably could include the thread in the geometry and simulate the screwing process so that all residual stresses are automatically considered in the analysis with actual loading.

I have frankly never heard anyone ask about "residual torque" beofre. Not in 40 years (god, that sounds a long time).

Why is "anyone" doing FEA on a nut ? Nuts (and screws) have defined allowable loads. What's the concern ??

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

rb - maybe they are a squirrel (sorry, couldn't resist).

Modelling the threads of a bolt/nut is, at best, a nightmare.

I have seen bolt preload modelled by using an initial temperature change with material CTEs. But it still takes a lot of "sorting out"

I did a small study on some weld studs. In the field some were fracturing from fatigue and it wasn't clear why. The claim was that they were over-stressing them in tension somehow.

My hypothesis was that the good ol' boys in our World Class Factory, were just grunting the nuts in place and paying no attention to the torque specs, which might be OK, if item was remaining in place.

So I had them weld up a bunch of studs to a plate and I got the nuts and started some twisting of my own, ti see if they snapped off just from tension.

What I found was that, if one just didn't stop turning the nut, the stud would elongate until the pitch on the threads was too much to fit in the nut. On the first install that would be no problem as the stud would have the full pre-load, but on any subsequent install the nut would hit the end of where the threads were good, the torque would shoot up, and the joint would not have the expected pre-load, allowing the part to shift back and forth until the stud snapped off.

What I didn't see, up to the point where the thread stretch was too much to fit anymore, was the body of the weld stud twisting. Maybe there is a tiny amount, but it doesn't seem consequential. For certain there is friction with the nut and the thread and the nut and the part and that friction will retain, for some time, the torque according to the amount of friction. But if the nut/screw unwound to remove that torque I doubt there would be a noticeable change in stress or pre-load and will be below all other contributors to variability.

In any case the residual torque cannot be more than friction at the screw thread radius can provide.