Giulio,
I can't see that there's anything wrong with your model, principally speaking. But when you do nonlinear analysis with several effects at the same time, such as here with contact, large deformations, plasticity, then the solver may sometimes have difficulties converging. I would typically introduce nonlinear effects into the model one by one. Start for example with LDA only, and ignore contacts. I would also start by running the analysis as a quick check (P-level 3, one pass). This is in fact a strategy if you have difficulties converging in pass 2, refine the mesh and run the model as "quick check". You will get P-level of 3 which is better than most conventional FE-softwares. With a fine mesh you may get sufficiently accurate results. Perhaps try some mesh controls to get more brick/wedge elements may helt reaching convergence. Nonlinear analyses are more sensitive to mesh quality.
Nonlinear analyses are generally less accurate, since there are more physical penomenae included in the analysis. It is more important to capture what's going on on a more general level. So if accurate convergence for stress for every location in the model is not too important, then a refined mesh+quick check is often good enough in non-linear analysis.
I have ran your analysis now to almost 50% of max displacment (without plasticity & contact), but I need to leave to pick up kids at daycare.... have a good weekend.
/Mats L/