A study of a unilateral and adhesive contact problem with normal compliance

Arezki Touzaline¹

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

Applicationes Mathematicae, Tome 41 (2014) no. 4, pp. 385-402.

Résumé

The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result in the case where the friction coefficient is small enough. The technique of proof is based on time-dependent variational inequalities, differential equations and the Banach fixed-point theorem. We also study a penalized and regularized problem which admits at least one solution and prove its convergence to the solution of the model when the penalization and regularization parameter tends to zero.

Détail

DOI : 10.4064/am41-4-8

Keywords: paper study quasistatic unilateral contact problem between elastic body foundation constitutive law nonlinear contact modelled normal compliance condition associated unilateral constraint coulombs friction law adhesion between contact surfaces taken account modelled surface variable bonding field whose evolution described first order differential equation establish variational formulation mechanical problem prove existence uniqueness result where friction coefficient small enough technique proof based time dependent variational inequalities differential equations banach fixed point theorem study penalized regularized problem which admits least solution prove its convergence solution model penalization regularization parameter tends zero