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A Viscoelastic Frictionless Contact Problem with Adhesion

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Języki publikacji
EN
Abstrakty
EN
We consider a mathematical model which describes the equilibrium between a viscoelastic body in frictionless contact with an obstacle. The contact is modelled with normal compliance, associated with Signorini's conditions and adhesion. The adhesion is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. The proof is based on arguments of evolution equations with multivalued maximal monotone operators, differential equations and the Banach fixed point theorem.
Słowa kluczowe
Rocznik
Strony
53--66
Opis fizyczny
Bibliogr. 33 poz.
Twórcy
autor
  • Faculté de Mathématiques, USTHB, Laboratoire de Systèmes Dynamiques, BP 32 El Alia, Bab-Ezzouar 16111, Algeria
Bibliografia
  • [1] L.-E. Andersson, Existence results for quasistatic contact problems with Coulomb friction, Appl. Math. Optim. 42 (2000), 169–202.
  • [2] M. Barboteu, X. Cheng and M. Sofonea, Analysis of a contact problem with unilateral constraint and slip-dependent f, Math. Mech. Solids (2014) (online).
  • [3] M. Barboteu, W. Han and M. Sofonea, A frictionless contact problem for viscoelastic materials, J. Appl. Math. 2 (2002), 1–21.
  • [4] V. Barbu, Optimal Control of Variational Inequalities, Res. Notes in Math. 100, Pitman, 1984.
  • [5] L. Cangémi, Frottement et adhérence: modèle, traitement numérique et application à l’interface fibre/matrice, Ph.D. thesis, Univ. Méditerranée, Aix Marseille I, 1997.
  • [6] O. Chau, J. R. Fernández, M. Shillor and M. Sofonea, Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion, J. Comput. Appl. Math. 159 (2003), 431–465.
  • [7] O. Chau, M. Shillor and M. Sofonea, Dynamic frictionless contact with adhesion, J. Appl. Math. Phys. 55 (2004), 32–47.
  • [8] M. Cocu, E. Pratt and M. Raous, Formulation and approximation of quasistatic frictional contact, Int. J. Engrg. Sci. 34 (1996), 783–798.
  • [9] M. Cocu and R. Rocca, Existence results for unilateral quasistatic contact problems with friction and adhesion, Math. Model. Numer. Anal. 34 (2000), 981–1001.
  • [10] M. Cocu, M. Schyvre and M. Raous, A dynamic unilateral contact problem with adhesion and friction in viscoelasticity, Z. Angew. Math. Phys. 61 (2010), 721–743.
  • [11] S. Drabla and Z. Zellagui, Analysis of a electro-elastic contact problem with friction and adhesion, Studia Univ. Babes-Bolyai Math. 54 (2009), 75–99.
  • [12] G. Duvaut, Équilibre d’un solide élastique avec contact unilatéral et frottement de Coulomb, C. R. Acad. Sci. Paris 290 (1980), 263–265.
  • [13] G. Duvaut et J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972.
  • [14] C. Eck, J. Jarušek and M. Krbec, Unilateral Contact Problems. Variational Methods and Existence Theorems, Pure Appl. Math. 270, Chapman & Hall/CRC, Boca Raton, FL, 2005.
  • [15] J. R. Fernández, M. Shillor and M. Sofonea, Analysis and numerical simulations of a dynamic contact problem with adhesion, Math. Comput. Modelling 37 (2003), 1317–1333.
  • [16] M. Frémond, Adhérence des solides, J. Mécanique Théor. Appl. 6 (1987), 383–407.
  • [17] M. Frémond, Équilibre des structures qui adhèrent à leur support, C. R. Acad. Sci. Paris Sér. II 295 (1982), 913–916.
  • [18] M. Frémond, Non-Smooth Thermomechanics, Springer, Berlin, 2002.
  • [19] J. Han, Y. Li and S. Migórski, Analysis of an adhesive contact problem for viscoelastic materials with long memory, J. Math. Anal. Appl. 427 (2015), 646–668.
  • [20] J. Jarušek and M. Sofonea, On the solvability of dynamic elastic-visco-plastic contact problems, Z. Angew. Math. Mech. 88 (2008), 3–22.
  • [21] J. Jarušek and M. Sofonea, On the solvability of dynamic elastic-visco-plastic contact problems with adhesion, Ann. Acad. Romanian Scientists Math. Appl. 1 (2009), 191–214.
  • [22] S. Migórski and A. Ochal, Dynamic bilateral contact problem for viscoelastic piezoelectric materials with adhesion, Nonlinear Anal. 69 (2008), 495–509.
  • [23] S. Migórski, A. Ochal and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Adv. Mech. Math. 26, Springer, 2013.
  • [24] S. A. Nassar, T. Andrews, S. Kruk and M. Shillor, Modelling and simulations of a bonded rod, Math. Comput. Modelling 42 (2005), 553–572.
  • [25] 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.
  • [26] R. Rocca, Analyse et numérique de problèmes quasi-statiques de contact avec frottement local de Coulomb en élasticité, thèse, Aix Marseille 1, 2005.
  • [27] J. Rojek and J. J. Telega, Contact problems with friction, adhesion and wear in orthopeadic biomechanics. I: General developments, J. Theor. Appl. Mech. 39 (2001), 655–677.
  • [28] M. Sofonea, W. Han and M. Shillor, Analysis and Approximation of Contact Problems with Adhesion or Damage, Pure Appl. Math. 276, Chapman & Hall/CRC, Boca Raton, FL, 2006.
  • [29] M. Sofonea and T. V. Hoarau-Mantel, Elastic frictionless contact problems with adhesion, Adv. Math. Sci. Appl. 15 (2005), 49–68.
  • [30] M. Sofonea and A. Matei, An elastic contact problem with adhesion and normal compliance, J. Appl. Anal. 12 (2006), 19–36.
  • [31] N. Strömberg, Continum thermodynamics of contact friction and wear, Ph.D. thesis, Linköping Univ., 1995.
  • [32] A. Touzaline, Analysis of a frictional contact problem with adhesion for nonlinear elastic materials I, Bull. Soc. Sci. Lettres Łódz Rech. Déformations 56 (2008), 61–74.
  • [33] A. Touzaline, Frictionless contact problem with finite penetration for elastic materials, Ann. Polon. Math. 98 (2010), 23–38.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-78a42829-950b-4dbd-a49b-823af29fe18b
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