A DEDUCTIVE THEORY OF FRICTION .2. MATHEMATICAL STUDY

The contact problem between two solid bodies has been studied, conside ring the existence of a third thin body separating the two bodies, wit h a viscoplastic behaviour law of Norton-Hoff type. The limit problem corresponding to the first order solution of the asymptotic problem is investigated, from the mathematical point of view. Several equivalent variational formulations of the model are derived. The existence and uniqueness of the solution of the material surface model are then stud ied. Lastly, error estimates between the three-dimensional problem and the limit two-dimensional model are obtained.