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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-3,
author = {Mohamed Selmani and Lynda Selmani},
title = {A Dynamic Frictionless Contact Problem with Adhesion and Damage},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {55},
year = {2007},
pages = {17-34},
zbl = {1114.35130},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-3}
}
Mohamed Selmani; Lynda Selmani. A Dynamic Frictionless Contact Problem with Adhesion and Damage. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 17-34. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-3/