Accepted for publication in JNEEA

Analysis of a quasistatic thermo-viscoelastic piezoelectric contact problem


T. Hadj Ammar

Department of Mathematics, Faculty of Exact Sciences, University of El Oued, P.O. Box 789, El Oued 39000, Algeria

Received on March 27, 2019, revised version on January 12, 2020
Accepted on January 2, 2020 (with modifications)

Communicated by Maximilian F. Hasler

Abstract.  This paper deals with the study of a quasistatic problem of friction contact between twothermo-viscoelastic piezoelectric bodies with long-term memory. The contact 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 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 equalities, a classical existence and uniqueness result on parabolic equalities, differential equations and fixed point theorem.
Keywords: thermo-viscoelastic piezoelectric material, adhesion, Coulomb’s law of friction, normal compliance, fixed point.
2010 Mathematics Subject Classification:   49J40, 74H20, 74H25.

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