Regularity of solutions to a dynamic frictionless contact problem with normal compliance

2004 ◽  
Vol 59 (7) ◽  
pp. 1063-1075 ◽  
Author(s):  
K KUTTLER ◽  
M SHILLOR
Keyword(s):  
Contact Problem ◽  
Regularity Of Solutions ◽  
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.

scholarly journals Regularity of solutions to a contact problem

1998 ◽  
Vol 350 (10) ◽  
pp. 4053-4063 ◽  
Author(s):  
Russell M. Brown ◽  
Zhongwei Shen ◽  
Peter Shi
Keyword(s):  
Contact Problem ◽  
Regularity Of Solutions

A dynamic elastic-visco-plastic unilateral contact problem with normal damped response and Coulomb friction

2010 ◽  
Vol 21 (3) ◽  
pp. 229-251 ◽  
Author(s):  
CHRISTOF ECK ◽  
JIŘÍ JARUŠEK ◽  
MIRCEA SOFONEA
Keyword(s):  
Contact Problem ◽  
Variational Equation ◽  
Auxiliary Problem ◽  
Regularity Of Solutions ◽  
Normal Velocity ◽  
Response Condition ◽  
The Coefficient Of Friction ◽  
The Galerkin Method ◽  
System Coupling ◽  
Normal Damped Response

We consider a dynamic frictional contact problem between an elastic-visco-plastic body and a foundation. The contact is modelled with a normal damped response condition of such a type that the normal velocity is restricted with unilateral constraint, associated with the Coulomb law in which the coefficient of friction may depend on the velocity. We derive a variational formulation of the problem which has the form of a system coupling an integro–differential equation for the stress field with an evolutionary variational inequality for the displacement field. This inequality is approximated by a variational equation using a smoothing of the friction and the penalty approximation of the unilateral condition. The existence of a weak solution to the variational equation is proved by the Galerkin method for an auxiliary problem with given viscoplastic part of the stress and a fixed point argument. The solvability of the original problem is proved by passing to the limit of the penalty parameter and the smoothing parameter. This convergence is based on a certain regularity of solutions which is verified with the use of a local rectification of the boundary and a translation method.

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