Published online by Cambridge University Press: 09 November 2015
In this paper, we study a quasi-static frictional contact problem for a viscoelastic body with damage effect inside the body as well as normal compliance condition and multi-valued friction law on the contact boundary. The considered friction law generalizes Coulomb friction condition into multi-valued setting. The variational–hemi-variational formulation of the problem is derived and arguments of fixed point theory and surjectivity results for pseudo-monotone operators are applied, in order to prove the existence and uniqueness of solution.
The research was supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118, the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under grant no. W111/7.PR/2012 and the National Science Center of Poland under Maestro Advanced Project no. DEC-2012/06/A/ST1/00262 and the project Polonium Mathematical and Numerical Analysis for Contact Problems with Friction 2014/15 between the Jagiellonian University and Université de Perpignan Via Domitia.