Numerical modelling of a dynamic contact problem with normal damped response and unilateral constraint

We consider a mathematical model which describes the dynamic evolution of a viscoelastic body in frictional contact with an obstacle. The contact is modelled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb’s law of dry friction. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we use a penalty method to approximate the constraint. Then, we provide numerical simulations in the study of a two-dimensional example and compare the penalty model with the original one.