A quasistatic contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline¹

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

Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 39-52.

Résumé

We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness of a weak solution if the friction coefficient is sufficiently small. The proof is based on time-dependent variational inequalities, differential equations and the Banach fixed point theorem.

Détail

DOI : 10.4064/am37-1-3

Keywords: consider mathematical model which describes contact between deformable body foundation contact frictional modelled version normal compliance condition associated coulombs law dry friction which adhesion contact surfaces taken account evolution bonding field described first order differential equation materials behaviour modelled nonlinear viscoelastic constitutive law derive variational formulation mechanical problem prove existence uniqueness weak solution friction coefficient sufficiently small proof based time dependent variational inequalities differential equations banach fixed point theorem