A quasistatic frictional problem with a normal compliance penalization term

A contact problem with friction for an elastic body, which under the influence of volume and surfaces forces is in contact with a rigid foundation, is considered. Outside the contact region, the equations of linearized elasticity is used. On the contact surface, a so-called Signorini condition of non-penetration and a Coulomb friction law is posed. In such an approach, considerable problems can be encountered. To solve these problems, the Signorini conditions are relaxed, to allow penetration but penalized it with the so-called normal compliance term. The evolution of a quasistatic problem with these normal compliance terms is discussed.