Hemivariational Inequality And Applications To Contact Mechanics

The dissertation investigates a type of hyperbolic hemivariational inequality and its applications to viscoelastic contact mechanics.In chapter two, we investigate the following hemivariational inequality: This is a type of hyperbolic hemivariational inequality. We prove the existence result by embedding the problem into a class of second-order evolution inclusion and by applying a surjectivity result for multivalued operators.In chapter three, we investigate the dynamic frictional contact problem between a viscoelastic-piezoelectric body and a foundation. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential. We state the existence result on the contact problem.In chapter four, we investigate the quasistatic process of frictional contact between a deformable body and a foundation. The body is assumed to be viscoelastic with long memory. The contact is modelled with a general normal compliance condition. The dependence of the the normal stress on the normal displacement is assumed to have nonmonotone character of the subdifferential form. We model the frictional contact assuming that the tangential shear on the contact surface is given as a nonmonotone and possibly multivalued function of the tangential displacement. We also consider the damage of the material. The effect due to the damage leads to decrease the carrying capacity of the body. The effective functioning and safety of a mechanical system may be deteriorated by this decrease as the material undergoes damaged. We derive the variational formulation of the problem, which is in the form of a system coupling a parabolic equation and a hemivariational inequality. We state and prove our main existence and uniqueness result.