Electron. J. Diff. Equ., Vol. 2014 (2014), No. 222, pp. 1-21.

Frictional contact problems for electro-viscoelastic materials with long-term memory, damage, and adhesion

Tedjani Hadj Ammar, Benyattou Benabderrahmane, Salah Drabla

We consider a quasistatic contact problem between two electro-viscoelastic bodies with long-term memory and damage. The contact is frictional and is modelled with a version of normal compliance condition and the associated Coulomb's law of friction in which the adhesion of contact surfaces is taken into account. We derive a variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, a classical existence and uniqueness result on parabolic inequalities, and Banach fixed point theorem.

Submitted May 20, 2014. Published October 21, 2014.
Math Subject Classifications: 49J40, 74H20, 74H25.
Key Words: Electro-viscoelastic material with long-term memory; damage; adhesion; friction contact; normal compliance; variational inequality; fixed point.

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Tedjani Hadj Ammar
Departement of Mathematics
Faculty of Sciences and Technology
University of El-Oued, 39000 El-Oued, Algeria
email: hat_olsz@yahoo.com
Benyattou Benabderrahmane
Department of Mathematics
Faculty of Mathematics and Informatics
M'Sila University, Algeria
email: bbenyattou@yahoo.com
Salah Drabla
Department of Mathematics
Faculty of Sciences
University of Sétif, 19000 Sétif, Algeria
email: drabla_s@yahoo.fr

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