# Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topCocu, 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

top- L. Cangémi, Frottement et adhérence: modèle, traitement numérique et application à l'interface fibre matrice. PhD thesis, University of Aix-Marseille II (1997).
- 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.
- 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.
- 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.
- R. Rocca and M. Cocu, Existence and approximation of a solution to quasistatic Signorini problem with local friction. Int. J. Engrg. (to appear).
- 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).
- Andersson L.-E, Existence results for quasistatic contact problems with Coulomb friction. Appl. Math. Optim. (to appear).
- M. Cocu, E. Pratt and M. Raous, Formulation and approximation of quasistatic frictional contact. Int. J. Engrg. Sci.34 (1996) 783-798.
- J. Jarušek, Contact problems with bounded friction coercive case. Czechoslovak Math. J.33 (1983) 237-261.
- C. Eck and J. Jarušek, Existence results for the static contact problem with Coulomb friction, Math. Models Methods Appl. Sci.8(1998) 445-468.
- R.A. Adams, Sobolev spaces. Academic Press, New York (1975).
- J.L. Lions and E. Magenes, Problèmes aux limites non homogènes, Vol. I. Dunod, Paris (1967).
- E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. I. Springer Verlag, New York (1993).

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