We consider a quasistatic contact problem between a linear elastic body and a foundation. The contact is modelled with the Signorini condition and the associated non-local Coulomb friction law in which the adhesion of the contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation of the mechanical problem and prove existence of a weak solution if the friction coefficient is sufficiently small. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments, differential equations and the Banach fixed point theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-8,
author = {Arezki Touzaline},
title = {A quasistatic unilateral and frictional contact problem with adhesion for elastic materials},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {107-127},
zbl = {1158.74037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-8}
}
Arezki Touzaline. A quasistatic unilateral and frictional contact problem with adhesion for elastic materials. Applicationes Mathematicae, Tome 36 (2009) pp. 107-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-8/