Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

Marius Cocu; Rémi Rocca

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 5, page 981-1001
  • ISSN: 0764-583X

Abstract

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We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction and adhesion on a part of his boundary. After discretizing the variational formulation with respect to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting technique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic solution by passing to the limit with respect to time.

How to cite

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Cocu, Marius, and Rocca, Rémi. "Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion." ESAIM: Mathematical Modelling and Numerical Analysis 34.5 (2010): 981-1001. <http://eudml.org/doc/197417>.

@article{Cocu2010,
abstract = { We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction and adhesion on a part of his boundary. After discretizing the variational formulation with respect to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting technique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic solution by passing to the limit with respect to time. },
author = {Cocu, Marius, Rocca, Rémi},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Friction; adhesion; local Coulomb law; unilateral contact; quasistatic problem.; two-dimensional elastic body; local friction; variational formulation; smoothing technique; shifting technique; existence of incremental solutions; regularization parameter; existence of quasistatic solution},
language = {eng},
month = {3},
number = {5},
pages = {981-1001},
publisher = {EDP Sciences},
title = {Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion},
url = {http://eudml.org/doc/197417},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Cocu, Marius
AU - Rocca, Rémi
TI - Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 5
SP - 981
EP - 1001
AB - We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction and adhesion on a part of his boundary. After discretizing the variational formulation with respect to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting technique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic solution by passing to the limit with respect to time.
LA - eng
KW - Friction; adhesion; local Coulomb law; unilateral contact; quasistatic problem.; two-dimensional elastic body; local friction; variational formulation; smoothing technique; shifting technique; existence of incremental solutions; regularization parameter; existence of quasistatic solution
UR - http://eudml.org/doc/197417
ER -

References

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  1. L. Cangémi, Frottement et adhérence: modèle, traitement numérique et application à l'interface fibre matrice. PhD thesis, University of Aix-Marseille II (1997).  
  2. M. Raous, L. Cangémi and M. Cocu, Un modèle couplant adhérence et frottement pour le contact unilatéral entre deux solides déformables. C. R. Acad. Sci., Paris, Série II b, t. 325 (1997) 503-509.  
  3. M. Raous, L. Cangémi and M. Cocu, A consistent model coupling adhesion friction and unilateral contact. Comput. Methods Appl. Mech. Engrg.177 (1999) 383-399.  
  4. R. Rocca, Existence of a solution for a quasistatic problem of unilateral contact with local friction. C. R. Acad. Sci., Paris, Série I. 328 (1999) 1253-1258.  
  5. R. Rocca and M. Cocu, Existence and approximation of a solution to quasistatic Signorini problem with local friction. Int. J. Engrg. (to appear).  
  6. R. Rocca, Analyse mathématique et numérique de problèmes quasi statique de contact unilatéral avec frottement local de Coulomb en élasticité, Ph.D. Thesis. Université d'Aix Marseille I (2000).  
  7. Andersson L.-E, Existence results for quasistatic contact problems with Coulomb friction. Appl. Math. Optim. (to appear).  
  8. M. Cocu, E. Pratt and M. Raous, Formulation and approximation of quasistatic frictional contact. Int. J. Engrg. Sci.34 (1996) 783-798.  
  9. J. Jarušek, Contact problems with bounded friction coercive case. Czechoslovak Math. J.33 (1983) 237-261.  
  10. C. Eck and J. Jarušek, Existence results for the static contact problem with Coulomb friction, Math. Models Methods Appl. Sci.8(1998) 445-468.  
  11. R.A. Adams, Sobolev spaces. Academic Press, New York (1975).  
  12. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes, Vol. I. Dunod, Paris (1967).  
  13. E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. I. Springer Verlag, New York (1993).  

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