A frictionless contact problem for elastic-visco-plastic materials with adhesion and thermal effects

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Authors :

Tedjani Hadj Ammar 1 * and Khezzani Rimi 2

Author Address :

1,2 Department of Mathematics, University of El-Oued, El Oued 39000, Algeria.

*Corresponding author.

Abstract :

We consider a mathematical problem for frictionless contact between a thermo-elastic-viscoplastic body with adhesion and an obstacle. We employ the thermo-elastic-viscoplastic with damage constitutive law for the material. The evolution of the damage is described by an inclusion of parabolic type. The evolution of the adhesion field is governed by the differential equation {small $ oldsymbol{ dot{eta }= H_{ad}ig(eta,xi_{eta},R_{ u}(u_{ u}),oldsymbol{R}_{ au}(oldsymbol{u}_{ au})ig)} $}. 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 uniqueness result on parabolic inequalities, differential equations and fixed point arguments.

Keywords :

Damage, adhesion, normal compliance, temperature, elastic-visco-plastic materials.

DOI :

10.26637/MJM0703/0002

Article Info :

Received : January 11, 2019; Accepted : May 21, 2019.

 

 

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