Abdelbaki Merouani, Farid Messelmi
We consider a mathematical model that describes the dynamic evolution of damage in elastic-thermo-viscoplastic materials with displacement-traction, and Neumann and Fourier boundary conditions. We derive a weak formulation of the system consisting of a motion equation, an energy equation, and an evolution damage inclusion. This system has an integro-differential variational equation for the displacement and the stress fields, and a variational inequality for the damage field. We prove existence and uniqueness of the solution, and the positivity of the temperature.
Submitted July 20, 2010. Published September 8, 2010.
Math Subject Classifications: 74H20, 74H25, 74M15, 74F05, 74R20.
Key Words: Damage field; temperature; elastic-thermo-viscoplastic; variational inequality.
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| Abdelbaki Merouani |
Departement de Mathematiques, Univerisite de Bordj Bou Arreridj
Bordj Bou Arreridj 34000, Algeria
| Farid Messelmi |
Departement de Mathematiques, Univerisite Zian Achour de Djelfa
Djelfa 17000, Algeria
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