Modeling and simulations for quasistatic frictional contact of a linear 2D bar

This work considers a mathematical model that describes quasistatic evolution of an elastic
2D bar that may come in frictional contact with a deformable foundation. We present the
model and some of its underlying assumptions. In particular, the novelty in the model is
that both vertical and horizontal motions are taken into account, which makes it especially
useful when frictional contact is concerned. Contact is described with the normal compliance
condition and friction with the Coulomb law of dry friction.We introduce a hybrid variational
formulation of the problem and a numerical discretization based on a uniform time step and
the finite element method in space. The numerical algorithm has been implemented, and
we present computer simulations that illustrate the mechanical behavior of the system with
emphasis on frictional aspects of the problem.