A Dynamic Frictionless Contact Problem with Adhesion and Damage
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 17-34
MSC: 35L70, 74M15, 74F25, 74H20.
DOI: 10.4064/ba55-1-3
Abstract
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.
