Abstract
We consider a dynamic frictionless contact problem between an elastic-viscoplastic body and a reactive foundation. The contact is modelled with normal compliance. The material is elastic-viscoplastic with two internal variables which may describe a temperature parameter and the damage of the system caused by plastic deformations. We derive a weak formulation of the system consisting of a motion equation, an energy equation, and an evolution damage inclusion. We prove existence and uniqueness of the solution, and the positivity of the temperature. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and unique- ness result on parabolic type inequalities, differential equations and fixed-point arguments.
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