Open AccessAnalysis of a Unilateral Contact Problem with Normal Compliance
Author(s) -
Arezki Touzaline,
Rachid Guettaf
Publication year - 2014
Publication title -
analele universităţii din timişoara. seria matematică-informatică/analele universităţii de vest din timişoara. seria matematică-informatică
Language(s) - English
Resource type - Journals
eISSN - 1841-3307
pISSN - 1841-3293
DOI - 10.2478/awutm-2014-0010
Subject(s) - uniqueness , unilateral contact , quasistatic process , mathematics , bounded function , constraint (computer aided design) , coulomb's law , nonlinear system , constant (computer programming) , mathematical analysis , variational inequality , coulomb , variational principle , physics , finite element method , geometry , computer science , quantum mechanics , thermodynamics , programming language , electron
The paper deals with the study of a quasistatic unilateral contact problem between a nonlinear elastic body and a foundation. The contact is modelled with a normal compliance condition associated to unilateral constraint and the 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 coefficient of friction is bounded by a certain constant. The technique of the proof is based on arguments of time-dependent variational inequalities, differential equations and fixed-point theorem