JT,
I worked on the Space Shuttle program at Rockwell/Boeing for a few years (and enjoyed it). The guy that sat in the office next to me was the engineer responsible for the Shuttle's tires, which are supplied by Michelin. Michelin claims that the shuttle MLG tires are the most high performance tires ever produced. The MLG tires must be replaced after each landing of the shuttle.
As for structural analysis of tires, I know a PhD that does FEA and was involved in the original development of the NASTRAN code. So he obviously knows his business. He says the most challenging work he ever did was developing an FEM process for an OEM tire company (Cooper maybe?).
You're right, modeling non-linear structures like tires is a real challenge.
riff_raff