Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 241 -- 267

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This work is licensed under a Creative Commons Attribution 4.0 International License.

A DYNAMIC CONTACT PROBLEM FOR THERMO-ELECTRO-VISOPLASTIC MATERIALS WITH DAMAGE AND INTERNAL STATE VARIABLE

Laid Maiza, Tedjani Hadj Ammar and Mohamed Laid Gossa

Abstract. This work studies a mathematical model involving a dynamic contact between two thermo-elasto-viscoplastic piezoelectric bodies with internal state variables and damage. The contact is modelled with normal compliance condition and adhesion effect of contact surfaces. We derive variational formulation of the problem and we prove an existence and uniqueness result of the weak solution. The proof is based on classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.

2020 Mathematics Subject Classification: 35Q74; 47H10; 49J40; 74D10
Keywords: thermo-elasto-viscoplastic piezoelectric materials; internal state variable; fixed point; adhesion; damage; normal compliance; weak solution.

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Laid Maiza
Laboratory of Applied Mathematics, Department of Mathematics
University Kasdi Merbah,30000 Ouargla, Algeria.
e-mail: maiza.laid@univ-ouargla.dz

Tedjani Hadj Ammar
Departement of Mathematics, University of El-Oued,
39000 El-Oued, Algeria.
e-mail: hadjammar_tedjani@univ-eloued.dz

Mohamed Laid Gossa
Department of Mathematics, University of Khenechla,
Khenechla, Algeria.
e-mail: gossa.med.laid@gmail.com



http://www.utgjiu.ro/math/sma