You might revisit your linear results and see if any of your materials are going past yield or UTS. If stresses are getting into high-curvature parts of the stress-strain curve, it could take a while.
I agree. Other usual suspects in the nonlinear study are curves and no penetration contact. Auto-stepping the time increment vs. user defined time step is also a frequent peril. I would animate the last time step's displacement plot and see if it behaves as intended. If buckling or other sudden behavior is observed, the arc-length control option may help reconcile big jumps in displacement over small time steps.
Y'all seem to have nailed the problem exactly. The stresses should be right near the top of the curve, and I've defined some no penetration contact sets as well. Sounds like that combination is going to result in a slow analysis.
Anything I can do to help it along? I'm vaugely familar with time steps, but I'm unaware of any guidelines as to how or when to change it from autostepping. I'm even less familiar with the arc-length control option. What exactly does it do? Is there a time when I should NOT use it?
What did the displacement animation inform? I would halve or quarter the model, mesh and re-run. You may have an element problem where two nodes are "tangled". Try remeshing with draft elements to get faster return during troubleshooting. Scale back up to full model when the problem is solved and apply the fix everywhere.
Others can delve into arc-length control's mathematics. ("...Equilibrium path..." ) Strategically, its used in situations where very large stiffness changes occur during the study, as in buckling. By default it is not used because it has more number crunching to do per step. I brought it up mainly because stalled solving after t=0 reminded of its use. That simulation was predicting buckling after arc-length was switched on was an eye opener in many cases.
By curve, I meant the relationship between loads and time ie. force vs. time. By default the relation is 1 to 1. By user definition, it can be exotic and can be a source of problems. By the same token, it can be very gentle.
From the linear study you said you did prior, the clue to find is which no penetration contact is producing the biggest nonlinearity. Process of elimination can be used if all of them look equally nonlinear. If just one is found to cause the problem, one possibility is to increase the friction coefficient.
If symmetry is employed as a boundary condition, use loads proportional to the reduced area caused by symmetric geometry.