Treatment of Contact Constraints

We now turn our attention to an important aspect of solving tire problems - the treatment of contact constraints. The contact problem to be solved is one of the two bodies contacting across their respective surfaces. The impenetrability of the two bodies (normal contact) will manifest itself as a set of unilateral constraints 

The frictional behavior of the two contacting bodies (we consider Coulomb friction here) is represented by the tangential contact constraints  

the discrete representation of the contact constraints expressed in Eqs. (21d) and (22d) are 

Focusing now on the enforcement of these constraints, we consider the similarity of the discrete contact constraint Eqs. (24a) and (24b) and the incompressibility constraint (8.12). 

Associating an index k with this outer constraint loop, an incremental kinematic prescription of the gap removal is utilized via 

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