Dynamic evolution of damage in elastic-thermo-viscoplastic materials - Abdelbaki Merouani (Electronic Journal of Differential Equations, 2010)
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.