Dynamic Contact of Viscoelastic Bodies with Two Obstacles: Mathematical and Numerical Approaches

The motion of viscoelastic (Kelvin-Voigt model) bodies between an upper and a lower obstacle is studied both mathematically and numerically. The two obstacles are assumed to be stationary perfect rigid, therefore, Signorini contact conditions are imposed at each obstacle, which can be interpreted as a couple of complementarity conditions (CCs). The convergence of numerical trajectories for general dimensional problems is shown based on the box constrained variational inequality (VI) which is equivalent to the two CCs. A one-dimensional example is provided. Unlike higher dimensional cases, different perspectives are used to prove the results of its existence. Numerical results are also presented and discussed, showing a typical behavior of the system