A viscoelastic contact problem with normal damped response and friction

B. Awbi; El H. Essoufi; M. Sofonea

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 3, page 233-246
  • ISSN: 0066-2216

Abstract

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We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.

How to cite

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Awbi, B., Essoufi, El H., and Sofonea, M.. "A viscoelastic contact problem with normal damped response and friction." Annales Polonici Mathematici 75.3 (2000): 233-246. <http://eudml.org/doc/208397>.

@article{Awbi2000,
abstract = {We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.},
author = {Awbi, B., Essoufi, El H., Sofonea, M.},
journal = {Annales Polonici Mathematici},
keywords = {variational problem; monotone operator; frictional contact; viscoelastic material; normal damped response; fixed point; viscoelastic body; evolution problem; quasistatic contact; variational formulation; local friction law; existence; unique weak solution; monotone operators; fixed point argument; continuous dependence on boundary conditions},
language = {eng},
number = {3},
pages = {233-246},
title = {A viscoelastic contact problem with normal damped response and friction},
url = {http://eudml.org/doc/208397},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Awbi, B.
AU - Essoufi, El H.
AU - Sofonea, M.
TI - A viscoelastic contact problem with normal damped response and friction
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 3
SP - 233
EP - 246
AB - We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.
LA - eng
KW - variational problem; monotone operator; frictional contact; viscoelastic material; normal damped response; fixed point; viscoelastic body; evolution problem; quasistatic contact; variational formulation; local friction law; existence; unique weak solution; monotone operators; fixed point argument; continuous dependence on boundary conditions
UR - http://eudml.org/doc/208397
ER -

References

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  10. [10] P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Basel, 1985. 
  11. [11] M. Raous, M. Jean and J. J. Moreau, Contact Mechanics, Plenum Press, New York, 1995. 
  12. [12] M. Rochdi, M. Shillor and M. Sofonea, A quasistatic viscoelastic contact problem with normal compliance and friction, J. Elasticity 51 (1998), 105-126. Zbl0921.73231
  13. [13] M. Rochdi, M. Shillor and M. Sofonea, A quasistatic contact problem with directional friction and damped response, Appl. Anal. 68 (1998), 409-422. Zbl0904.73055
  14. [14] M. Rochdi, M. Shillor and M. Sofonea, Analysis of a quasistatic viscoelastic problem with friction and damage, Adv. Math. Sci. Appl. 10 (2000), 173-189. Zbl0962.74044
  15. [15] M. Sofonea and M. Shillor, Variational analysis of quasistatic viscoplastic contact problems with friction, Comm. Appl. Anal., to appear. Zbl1084.74541

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