<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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. </p></abstract>

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.

Analysis of a Unilateral Contact Problem with Normal Compliance

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

Faculté des Sciences Campus Sud, UMBB-35000 Boumerdès, Algérie

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Analysis of a Unilateral Contact Problem with Normal Compliance"}

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...

Analysis of a Unilateral Contact Problem with Normal Compliance

Published Online: Dec 11, 2014

Page range: 157 - 171

Received: Apr 12, 2014

Accepted: Jul 26, 2014

DOI: https://doi.org/10.2478/awutm-2014-0010

Keywords
elastic, normal compliance, adhesion,friction, unilateral, weak solution

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Analysis of a Unilateral Contact Problem with Normal Compliance

Published Online: Dec 11, 2014

Page range: 157 - 171

Received: Apr 12, 2014

Accepted: Jul 26, 2014

DOI: https://doi.org/10.2478/awutm-2014-0010

Keywordselastic, normal compliance, adhesion,friction, unilateral, weak solution

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
elastic, normal compliance, adhesion,friction, unilateral, weak solution