I recommend looking at the File Exchange submission Simscape Multibody Contact Forces Library. It contains a library of blocks for use with Simscape Multibody that detect collision between various shapes, calculates the normal force and friction force on each part, and applies them to the colliding parts.
Below are a few animations that test models included in the submission. The Simscape Multibody Contact Forces Library contains the library for current and previous MATLAB releases.
Also look at the File Exchange Submission Vehicle Model with Delft-Tyre in Simscape Multibody that includes a full vehicle model that has 15 DOF, and it uses the free software Delft-Tyre to model the contact between the car and the road
Thanks,
--Steve
Two-wheeled robot:
Ball in spinning cone: