Dynamic frictional thermoviscoelastic contact problem with normal compliance and damage

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Khelifa Chadi ◽  
Mohamed Selmani
Keyword(s):  
Contact Problem ◽  
Normal Compliance

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 Analysis of a Dynamic Viscoelastic Contact Problem with Normal Compliance, Normal Damped Response, and Nonmonotone Slip Rate Dependent Friction

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Mikaël Barboteu ◽  
David Danan
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Slip Rate ◽  
Approximation Schemes ◽  
Discrete Approximation ◽  
Normal Compliance ◽  
Fully Discrete ◽  
Rate Dependent ◽  
Fully Discrete Approximation ◽  
Normal Damped Response

We consider a mathematical model which describes the dynamic evolution of a viscoelastic body in frictional contact with an obstacle. The contact is modelled with a combination of a normal compliance and a normal damped response law associated with a slip rate-dependent version of Coulomb’s law of dry friction. We derive a variational formulation and an existence and uniqueness result of the weak solution of the problem is presented. Next, we introduce a fully discrete approximation of the variational problem based on a finite element method and on an implicit time integration scheme. We study this fully discrete approximation schemes and bound the errors of the approximate solutions. Under regularity assumptions imposed on the exact solution, optimal order error estimates are derived for the fully discrete solution. Finally, after recalling the solution of the frictional contact problem, some numerical simulations are provided in order to illustrate both the behavior of the solution related to the frictional contact conditions and the theoretical error estimate result.

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