The reason you may not want to build a tire model is the solve time and material properties/material composition. I run a unix machine with 4 processors and 8 GB of ram and to solve contact/wheel model/tire model it takes well over 4 hours to solve and for most of us that is not feasible. Also, the tire model is very difficult/impossible to create and have accurate contact with the rim.
The tire/rim bead interface if a difficult interaction that is more difficult to model than at first glance. Dr. Stearns from Goodyear tire company, graduate from University of Akron, Ohio, did his doctoral thesis and derived the contact analysis from an eyebar loading method. Still the vertical and horizontal components of both the inboard and outboard bead seat are still difficult to define.
Good Luck
Tabor