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Quasi-Static Linear Thermo-Viscoelastic Process with Irregular Viscous Dissipation

Part of: Materials of strain-rate type and history type, other materials with memory Equations and systems of special type Coupling of solid mechanics with other effects

Published online by Cambridge University Press:  18 January 2017

Farid Messelmi ,
Abdelbaki Merouani  and
Hicham Abdelaziz
Farid Messelmi*
Affiliation:
Department of Mathematics and LDMM Laboratory, University Ziane Achour de Djelfa, Djelfa 17000, Algeria
Abdelbaki Merouani*
Affiliation:
Department of Mathematics, University of Bordj Bou Arreridj, Bordj Bou Arreridj 34000, Algeria
Hicham Abdelaziz*
Affiliation:
Department of Mathematics, University of Bordj Bou Arreridj, Bordj Bou Arreridj 34000, Algeria
*
*Corresponding author. Email:foudimath@yahoo.fr (F. Messelmi), badri_merouani@yahoo.fr (A. Merouani), hichem.abd21@gmail.com (H. Abdelaziz)
*Corresponding author. Email:foudimath@yahoo.fr (F. Messelmi), badri_merouani@yahoo.fr (A. Merouani), hichem.abd21@gmail.com (H. Abdelaziz)
*Corresponding author. Email:foudimath@yahoo.fr (F. Messelmi), badri_merouani@yahoo.fr (A. Merouani), hichem.abd21@gmail.com (H. Abdelaziz)
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Abstract

We consider a mathematical model which describes the quasi-static evolution of a thermo-viscoelastic linear body with taking into account the effects of internal forces which generate a non linear viscous dissipative function. We derive a variational formulation of the system of equilibrium equation and energy equation. An existence result of weak solutions was obtained in an appropriate function space.

Keywords

Thermo-viscoelasticityviscous dissipation

MSC classification

Secondary: 35M10: Equations of mixed type 74D05: Linear constitutive equations 74F05: Thermal effects
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 4 , August 2017 , pp. 924 - 943
Copyright
Copyright © Global-Science Press 2017 

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