Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 129, pp. 1-15.

Title: Dynamic evolution of damage in elastic-thermo-viscoplastic materials

Authors: Abdelbaki Merouani (Univ. de Bordj Bou Arreridj, Algeria)
         Farid Messelmi     (Univ. de Bordj Bou Arreridj, Algeria)

Abstract: 
 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 08, 2010.
Math Subject Classifications: 74H20, 74H25, 74M15, 74F05, 74R20.
Key Words: Damage field; temperature; elastic-thermo-viscoplastic;
           variational inequality.