Vol. LXXVII, 2 (2008)
p. 181 - 198

Analysis of a frictional contact problem with adhesion

Z. Lerguet, M. Sofonea and S. Drabla

Received: February 12, 2007;  Accepted: November 28, 2007;

Abstract.  We consider a mathematical model which describes the contact between a deformable body and an obstacle, the so-called foundation. The contact is frictional and is modelled with a version of normal compliance condition and the associated Coulomb's law of dry friction in which the 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 behavior is modelled with a nonlinear elastic constitutive law. We derive a variational formulation of the problem then, under a smallness assumption on the coefficient of friction, we prove the existence of a unique weak solution for the model. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach's fixed point theorem. Finally, we extend our results in the case when the piezoelectric effect is taken into account, i.e. in the case when the material's behavior is modelled with a nonlinear electro-elastic constitutive law.

Keywords: elastic material; frictional contact; normal compliance; adhesion; electro-elastic material; weak solution; variational inequality; differential equation; fixed point.  

AMS Subject classification: Primary: 74M10; 74M15  Secondary: 74F99; 74G25; 35J85

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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