Contact problem in thermo-elastic viscoplastic materials with damage

10.30495/maca.2024.2036276.1107
Volume 6, Issue 3
Autumn 2024
Pages 1-19

Document Type : Original Article

Author

University of El Oued, Laboratory of Operator Theory and PDE: Foundations and Applications, 39000, El Oued, Algeria

Abstract
We consider in this paper a quasi-static contact problem with a simplified Tresca model of slip-dependent coefficient of friction in nonlinear thermo-elastic-viscoplastic materials with damage. The evolution of the damage is described by an inclusion of parabolic type. We derive a variational formulation of the problem and prove the existence of a unique weak solution. The proof is based on classical existence and uniqueness results for parabolic inequalities, differential equations, and fixed point arguments.

Keywords

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  • Receive Date 21 July 2024
  • Revise Date 07 September 2024
  • Accept Date 19 September 2024