The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Contact With Adhesion between a Deformable Body and a Foundation


B. Teniou and M. Sofonea

Laboratoire de Mathematiques Appliquées et Modélisation,
Université Mentouri, Constantine 25000,

Laboratoire de Mathématiques et Physiques pour les Systémes,
Univesité de Perpignan,


The aim of this work is study a dynamic contact problem between a deformable body and a foundation where the deformations are supposed to be small. The contact is with adhesion and normal compliance. The behavior of this body is modeled by a nonlinear elastic-visco-plastic law. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the contact problem and we prove the existence and uniqueness of its solution. The proof is based on the construction of three intermediate problems and then we construct a contraction mapping whose unique fixed point will be the weak solution of the mechanical problem.

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