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It is possible to model such a problem. Lesson 8 of the Nonlinear manual deals with such a case, although it is somewhat simple. More complex models need significant time to set up and run.
Yes, this is very doable in nonlinear, but as Fernando says, it can take a bit of time to run. Having an accurate material model is very important, and the strain does not get too excessive. Forming an object around a large tool is a good application, but trying to deep draw or stamp a part with a die is getting too extreme (strain in the 100's of %) in general.