A frictionless contact problem for elastic–viscoplastic materials with normal compliance and damage

2002 ◽  
Vol 191 (44) ◽  
pp. 5007-5026 ◽  
Author(s):  
O. Chau ◽  
J.R. Fernández-Garcı́a ◽  
W. Han ◽  
M. Sofonea
Keyword(s):  
Contact Problem ◽  
Normal Compliance ◽  
Frictionless Contact

scholarly journals Analysis of electroelastic frictionless contact problems with adhesion

2006 ◽  
Vol 2006 ◽  
pp. 1-25 ◽  
Author(s):  
Mircea Sofonea ◽  
Rachid Arhab ◽  
Raafat Tarraf
Keyword(s):  
Contact Problem ◽  
Contact Problems ◽  
Time Dependent ◽  
Stiffness Coefficient ◽  
Normal Compliance ◽  
Unique Weak Solution ◽  
Frictionless Contact ◽  
Contact Surfaces ◽  
Signorini Contact ◽  
Variational Formulations

We consider two quasistatic frictionless contact problems for piezoelectric bodies. For the first problem the contact is modelled with Signorini's conditions and for the second one is modelled with normal compliance. In both problems the material's behavior is electroelastic and the adhesion of the contact surfaces is taken into account and is modelled with a surface variable, the bonding field. We provide variational formulations for the problems and prove the existence of a unique weak solution to each model. The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.

A piezoelectric contact problem with slip dependent friction and damage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abderrezak Kasri
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Normal Compliance ◽  
Electrically Conductive ◽  
Coulomb’S Law ◽  
Electrical Condition ◽  
Coulomb's Law

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

A dynamic frictionless contact problem using signorini like compliance laws

1997 ◽  
Vol 35 (12-13) ◽  
pp. 1245-1260
Author(s):  
G. Bayada ◽  
M. Chambat ◽  
A. Lakhal ◽  
L. Rochet
Keyword(s):  
Contact Problem ◽  
Frictionless Contact
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