| Abstract: |
| We consider a nonlinear viscoelastic rod that is in contact with a foundation along its length and with an obstacle at its end. The rod is subjected to body forces and, as a result, its mechanical state evolves.
We assume that the internal stress at the end of the rod depends on both its displacement and velocity, and that this relationship takes the form of a Clarke subdifferential inclusion. In a specific case, it coincides with the so-called damped normal compliance condition introduced recently in contact mechanics. This generalizes our previous model, in which the stress depends only on the velocity.
Our aim is twofold. The first is to construct an appropriate mathematical model that describes the evolution of the rod. The second is to prove the existence of a weak solution to the problem. To this end, we use a time discretization method for second-order inclusion with multivalued pseudomonotone operators, which constitutes the weak formulation of the problem. |
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