Abstract
In this paper, we study a class of dynamic thermal problems involving a frictional normal compliance adhesive contact model and a non-clamped condition for visco-elastic materials. The variational formulation of the problem leads to a general system defined by a second-order quasi-variational evolution inequality on the displacement field coupled with the two first-order evolution equations describing the evolution of the temperature and adhesion. We establish an existence and uniqueness result of the solution on displacement, temperature and adhesion. Then we provide a fully discrete numerical scheme of approximation and derive an error estimate. Finally, various numerical computations are included.
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