p. 181 - 198 Analysis of a frictional contact problem with adhesion
Z. Lerguet, M. Sofonea and S. Drabla Received: February 12, 2007;
Accepted: November 28, 2007;
Abstract.
We consider a mathematical model which describes the contact
between a deformable body and an obstacle, the so-called
foundation. The contact is frictional and is modelled with a
version of normal compliance condition and the associated
Coulomb's law of dry friction in which the adhesion of contact
surfaces is taken into account. The evolution of the bonding field
is described by a first order differential equation and the
material's behavior is modelled with a nonlinear elastic
constitutive law. We derive a variational formulation of the
problem then, under a smallness assumption on the coefficient of
friction, we prove the existence of a unique weak solution for the
model. The proof is based on arguments of time-dependent
variational inequalities, differential equations and Banach's
fixed point theorem. Finally, we extend our results in the case
when the piezoelectric effect is taken into account, i.e. in the
case when the material's behavior is modelled with a nonlinear
electro-elastic constitutive law.
Keywords:
elastic material; frictional contact; normal compliance; adhesion; electro-elastic material; weak solution; variational
inequality; differential equation; fixed point.
AMS Subject classification: Primary: 74M10; 74M15
Secondary: 74F99; 74G25; 35J85
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