Analysis of a quasistatic contact problem with wear and damage for thermo-viscoelastic materials

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Authors :

Ilyas Boukaroura1∗and Seddik Djabi2

Author Address :

1,2 Department of Mathematics, Ferhat Abbas- Setif1 University, Setif, 19000 , Algeria.

*Corresponding author.
 

Abstract :

We consider a quasistatic contact problem for an thermo visco-elastic body with wear and damage between a thermo-viscoelastic body and a rigid obstacle. The contact is frictional and bilateral which results in the wear and damage of contacting surface. The evolution of the wear function is described with Archard’s law.The evolution of the damage is described by an inclusion of parabolic type. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem. The proof is based on a classical existence and uniquness result on parabolic inéqualities, differentiel equations and fixed point argument.

Keywords :

thermoviscoelastic, variationel inequality, wear,damage field, fixed point.

DOI :

10.26637/MJM0602/0001

Article Info :

Received : February 15, 2018; Accepted : March 13, 2018.

 

 

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