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A dynamic prictionless contact problem with adhesion and damage

Selmani M., Selmani L.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 1

17-34

We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The proofs are based on the theory of evolution equations with monotone operators, a classical existence and uniqueness result for parabolic inequalities, and fixed point arguments.

Variational Analysis of a Frictional Contact Problem for the Bingham Fluid

Awbi B., Selmani L., Sofonea M.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 2

371-385

We consider a mathematical model which describes the flow of a Bingham fluid with friction. We assume a stationary flow and we model the contact with damped response and a local version of Coulomb's law of friction.The problem leads to a quasi-variational inequality for the velocity field. We establish the existence of a weak solution and, under additional assumptions, its uniqueness. The proofs are based on a new result obtained in (Motreanu and Sofonea, 1999). We also establish the continuous dependence of the solution with respect to the contact conditions.