Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 174, pp. 1-13.
Title: Frictionless contact problem with adhesion for nonlinear
elastic materials
Author: Arezki Touzaline (USTHB, Bab-Ezzouar, Algerie)
Abstract:
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.