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1 Bulletin of the Polish Academy of Sciences. Mathematics

1 2007

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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.