december 2021 Dynamic frictional thermoviscoelastic contact problem with normal compliance and damage
Khelifa Chadi, Mohamed Selmani
Bull. Belg. Math. Soc. Simon Stevin 28(2): 195-215 (december 2021). DOI: 10.36045/j.bbms.191105

Abstract

We study a dynamic problem describing the frictional contact between a thermoviscoelastic body and a foundation. The thermoviscoelastic constitutive law includes a damage effect described by the parabolic inclusion with the homogeneous Neumann boundary condition and a temperature effect described by the first order evolution equation. The contact is modeled with normal compliance condition with friction. We present a variational formulation of the problem and establish an existence and uniqueness of the weak solution. The proof is based on parabolic variational inequalities of first and second kind, first order evolutionary variational equations and fixed point arguments.

Citation

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Khelifa Chadi. Mohamed Selmani. "Dynamic frictional thermoviscoelastic contact problem with normal compliance and damage." Bull. Belg. Math. Soc. Simon Stevin 28 (2) 195 - 215, december 2021. https://doi.org/10.36045/j.bbms.191105

Information

Published: december 2021
First available in Project Euclid: 23 December 2021

Digital Object Identifier: 10.36045/j.bbms.191105

Subjects:
Primary: 74D10 , 74F05 , 74M10 , 74M15

Keywords: damage , dynamic process , fixed point , frictional contact , long memory , normal compliance , Thermoviscoelastic materials , Weak solution

Rights: Copyright © 2021 The Belgian Mathematical Society

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Vol.28 • No. 2 • december 2021
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