We consider a quasistatic frictionless contact problem for a nonlinear elastic body. The contact is modelled with Signorini's conditions. In this problem we take into account of the adhesion which is modelled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We derive a variational formulation of the mechanical problem and we establish an existence and uniqueness result by using arguments of time-dependent variational inequalities, differential equations and Banach fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of a penalized problem as the penalization parameter converges to 0.
An addendum was attached on December 22, 2011. It corrects some misprints and parts of Lemmas 3.1 and 3.2.
Submitted May 8, 2007. Published December 12, 2007.
Math Subject Classifications: 35J85, 49J40, 47J20, 74M15.
Key Words: Nonlinear elasticity; adhesive contact; frictionless; variational inequality; weak solution.
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| Arezki Touzaline |
Faculté de Mathématiques, USTHB BP 32 EL Alia
Bab-Ezzouar, 16111, Algérie
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