Mikael Barboteu (Université de Perpignan).
In this work, 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 compliance and unilateral constraint, associated to a rate slip-dependent version of
Coulomb’s law of dry friction.
In order to approximate the contact conditions, we consider a regularized problem wherein the contact is modelled by a standard
normal compliance condition without unilateral constraint.
For each problem, we derive a variational formulation and an existence result of the weak solution of the regularized problem is
obtained.
Then, we introduce a fully discrete approximation of the variational problem based on a finite element method and on a second
order time integration scheme.
Next, we prove the convergence of the weak solution of the regularized problem to the weak solution of the initial nonregularized
problem.
Under certain solution regularity assumptions, we derive an optimal order error estimate.
Furthermore, the solution of the resulting nonsmooth and nonconvex frictional contact problems is presented, based on
approximation by a sequence of nonsmooth convex programming problems.
Finally, some numerical simulations are provided in order to illustrate both the behavior of the solution related to the frictional
contact conditions and the convergence result.