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Analysis of a Dynamic Viscoelastic Contact Problem with Normal Compliance, Normal Damped Response, and Nonmonotone Slip Rate Dependent Friction
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-10-17
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Barboteu, Mikaël& Danan, David. 2016. Analysis of a Dynamic Viscoelastic Contact Problem with Normal Compliance, Normal Damped Response, and Nonmonotone Slip Rate Dependent Friction. Advances in Mathematical Physics،Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1095768
Modern Language Association (MLA)
Barboteu, Mikaël& Danan, David. Analysis of a Dynamic Viscoelastic Contact Problem with Normal Compliance, Normal Damped Response, and Nonmonotone Slip Rate Dependent Friction. Advances in Mathematical Physics No. 2016 (2016), pp.1-15.
https://search.emarefa.net/detail/BIM-1095768
American Medical Association (AMA)
Barboteu, Mikaël& Danan, David. Analysis of a Dynamic Viscoelastic Contact Problem with Normal Compliance, Normal Damped Response, and Nonmonotone Slip Rate Dependent Friction. Advances in Mathematical Physics. 2016. Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1095768
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095768