Numerical nodelling 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.