ANALYSIS OF A DYNAMIC CONTACT PROBLEM FOR ELECTRO-VISCOELASTIC MATERIALS WITH TRESCA'S FRICTION

ANALYSIS OF A DYNAMIC CONTACT PROBLEM FOR ELECTRO-VISCOELASTIC MATERIALS WITH TRESCA'S FRICTION

B. Douib, T. Hadj Ammar, A. Azeb Ahmed

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Abstract

We consider a mathematical model which describes the dynamic process of contact between two electro-viscoelastic bodies with damage. The contact is bilateral and is modeled with Tresca's friction law. The damage of the materials caused by elastic deformations. We derive a variational formulation for the model which is in the form of a system involving the displacement  eld, the electric potential and the damage. Then we provide the existence of a unique weak solution to the model. We also study the  nite element approximations of the problem and derive error estimates. Finally, we present numerical simulation results in the study of a two-dimensional example.

Keywords

Dynamic process, piezoelectric, monotone operator,  xed point, weak solu- tion, damage.