Comptes Rendus
no. 6
Analysis of viscoelastic contact with normal compliance, friction and wear diffusion
[Analyse d'un problème viscoélastique avec compliance normale, frottement et diffusion d'usure]

Présenté par : Évariste Sanchez-Palencia

Meir Shillor1  ; Mircea Sofonea2  ; J.Joachim Telega3
1 Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
2 Laboratoire de Théorie de Systèmes, Université de Perpignan, 52, avenue de Villeneuve, 66860 Perpignan, France
3 Inst. Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland
Comptes Rendus. Mécanique, Volume 331 (2003) no. 6, pp. 395-400.

Nous considérons un problème quasistatique de contact entre un corps viscoélastique et une fondation mobile. Le contact est avec usure et se modélise avec compliance normale et une loi de frottement sec. La principale nouveauté du modèle réside dans le fait qu'il prend en considération la diffusion des débris d'usure sur la surface potentielle de contact. Ce phénomème est rencontré en biomécanique orthopédique et il influence les propriétés des prothèses. Nous présentons une formulation variationnelle du problème et, sous une hypothèse de petitesse, nous présentons l'existence et l'unicité de la solution faible du modèle.

We consider a quasistatic problem of frictional contact between a viscoelastic body and a moving foundation. The contact is with wear and is modeled by normal compliance and a law of dry friction. The novelty in the model is that it allows for the diffusion of the wear debris over the potential contact surface. Such kind of phenomena arise in orthopaedic biomechanics and influence the properties of joint prosthesis. We derive a weak formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(03)00086-X
Keywords: Solids and structures, Nonlinear viscoelastic solid, Contact, Friction, Wear diffusion
Mot clés : Solides et structures, Solide viscoélastique non linéaire, Contact, Frottement, Diffusion d'usure
Meir Shillor 1 ; Mircea Sofonea 2 ; J.Joachim Telega 3

1 Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
2 Laboratoire de Théorie de Systèmes, Université de Perpignan, 52, avenue de Villeneuve, 66860 Perpignan, France
3 Inst. Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland 
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     title = {Analysis of viscoelastic contact with normal compliance, friction and wear diffusion},
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Meir Shillor; Mircea Sofonea; J.Joachim Telega. Analysis of viscoelastic contact with normal compliance, friction and wear diffusion. Comptes Rendus. Mécanique, Volume 331 (2003) no. 6, pp. 395-400. doi : 10.1016/S1631-0721(03)00086-X. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00086-X/

[1] J. Rojek; J.J. Telega Contact problems with friction, adhesion and wear in orthopaedic biomechanics. I: General developments, J. Theor. Appl. Mech., Volume 39 (2001), pp. 655-677

[2] J. Rojek; J.J. Telega; S. Stupkiewicz Contact problems with friction, adhesion and wear in orthopaedic biomechanics. II: Numerical implementation and application to implanted knee joints, J. Theor. Appl. Mech., Volume 39 (2001), pp. 680-706

[3] N. Strömberg; L. Johansson; A. Klarbring Derivation and analysis of a generalized standard model for contact friction and wear, Int. J. Solids Structures, Volume 33 (1996), pp. 1817-1836

[4] N. Kikuchi; T.J. Oden Contact Problems in Elasticity, SIAM, Philadelphia, 1988

[5] A. Klarbring; A. Mikelic; M. Shillor Frictional contact problems with normal compliance, Int. J. Engrg. Sci., Volume 26 (1988), pp. 811-832

[6] J.A.C. Martins; T.J. Oden Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws, Nonlinear Anal., Volume 11 (1987), pp. 407-428

[7] M. Shillor, M. Sofonea, J.J. Telega, Quasistatic viscoelastic contact with friction and wear diffusion, Quart. Appl. Math., to appear

[8] M. Rochdi; M. Shillor; M. Sofonea A quasistatic viscoelastic contact problem with normal compliance and friction, J. Elasticity, Volume 51 (1998), pp. 105-126

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