A class of thermal sub-differential contact problems

Abstract

We study a class of dynamic sub-differential contact problems with friction, and thermale ects, for time depending long memory visco-elastic materials, with or without the clamped condition.We describe the mechanical problem, derive its variational formulation, and after specifyingthe assumptions on the data and operators, we prove an existence and uniqueness of weak solutionon displacement and temperature fields. Then we present a fully discrete scheme for numerical approximationsof the different solutions, and provide analysis of error order estimates. Finally variousnumerical computations in dimension two will be given.

Keywords

• time depending thermo-visco-elasticity| sub-differential contact condition| non clamped condition| evolution variational inequality| numerical analysis| numerical computations