A quasi-static contact problem with friction in electro viscoelasticity with long-term memory body with damage and thermal effects.

Document Type : Research Paper


1 Laboratory of Operator Theory and PDE: Foundations and Applications, Faculty of Exact Sciences, University of El Oued, 39000, El Oued, Algeria

2 Department of Mathematics, University of El Oued, 39000 El Oued, Algeria


In this paper, we consider a mathematical model that describes the quasi-static process of contact between a piezoelectric body and a deformable foundation. A nonlinear thermo-electro-viscoelastic constitutive law with long term memory and damage is used and the contact is described with the normal compliance condition and a version of Coulomb’s law of friction. We derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field, the temperature field and the damage field, existence and uniqueness of a weak solution of the problem is proved. The proof is based on arguments of time-dependent variational inequalities, parabolic inequalities, differential equations and fixed points.


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Volume 13, Issue 2
July 2022
Pages 205-220
  • Receive Date: 12 August 2021
  • Revise Date: 07 December 2021
  • Accept Date: 25 January 2022