A quasistatic unilateral and frictional contact problem with adhesion for elastic materials

Arezki Touzaline¹

¹ Laboratoire de Systèmes Dynamiques Faculté de Mathématiques, USTHB BP 32 El Alia Bab Ezzouar, 16111, Algeria

Applicationes Mathematicae, Tome 36 (2009) no. 1, pp. 107-127

Résumé

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.

Détail

DOI : 10.4064/am36-1-8

Keywords: consider quasistatic contact problem between linear elastic body foundation contact modelled signorini condition associated non local coulomb friction law which adhesion contact surfaces taken account evolution bonding field described first order differential equation derive variational formulation mechanical problem prove existence weak solution friction coefficient sufficiently small proofs employ time discretization method compactness lower semicontinuity arguments differential equations banach fixed point theorem