A dynamic Tresca's frictional contact problem with damage for thermo elastic-viscoplastic bodies

Ilyas Boukaroura; Seddik Djabi

doi:10.24193/subbmath.2019.3.13

Authors

Ilyas Boukaroura Departement of mathematics, Mohamed Elbachir Elibrahimi- Bordj Bou Arreridj university
Seddik Djabi Department of Mathematics, Ferhat Abbas, Sétif 1 University

DOI:

https://doi.org/10.24193/subbmath.2019.3.13

Keywords:

elastic-viscoplastic, temperature, variationel inequality, fixed point

Abstract

We consider a dynamic contact problem between an elastic-viscoplastic body and a rigid obstacle. The contact is frictional and bilateral, the friction is modeled with Tresca's law with heat exchange. We employ the elastic-viscoplastic with damage constitutive law for the material. 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 inequalities, differentiel equations and fixed point argument.

Author Biographies

Ilyas Boukaroura, Departement of mathematics, Mohamed Elbachir Elibrahimi- Bordj Bou Arreridj university

Assistant professor
Seddik Djabi, Department of Mathematics, Ferhat Abbas, Sétif 1 University

Professor

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