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A piezoelectric contact problem with slip dependent friction and damage

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.
Wydawca
Rocznik
Strony
73--86
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • Département de Mathématiques, Faculté des Sciences, Université 20 Août 1955 - Skikda, B.P.26 Route El-Hadaiek-Skikda, Algeria
Bibliografia
  • [1] M. Barboteu and M. Sofonea, Analysis and numerical approach of a piezoelectric contact problem, Ann. Acad. Rom. Sci. Ser. Math. Appl. 1 (2009), no. 1, 7-30.
  • [2] R. C. Batra and J. S. Yang, Saint-Venant’s principle in linear piezoelectricity, J. Elasticity 38 (1995), no. 2, 209-218.
  • [3] H. Benaissa, E.-H. Essoufi and R. Fakhar, Analysis of a Signorini problem with nonlocal friction in thermo-piezoelectricity, Glas. Mat. Ser. III 51(71) (2016), no. 2, 391-411.
  • [4] H. Brezis, Équations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), no. 1, 115-175.
  • [5] G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972.
  • [6] M. Frémond and B. Nedjar, Damage in concrete: The unilateral phenomenon, Nuclear Eng. Design 156 (1995), 323-335.
  • [7] M. Frémond and B. Nedjar, Damage, gradient of damage and principle of virtual power, Internat. J. Solids Structures 33 (1996), no. 8, 1083-1103.
  • [8] J. Han and S. a. Migórski, A quasistatic viscoelastic frictional contact problem with multivalued normal compliance, unilateral constraint and material damage, J. Math. Anal. Appl. 443 (2016), no. 1, 57-80.
  • [9] T. Ikeda, Fundamentals of Piezoelectricity, Oxford University, Oxford, 1990.
  • [10] A. Kasri and A. Touzaline, Analysis of a dynamic contact problem with friction, damage and adhesion, Appl. Math. (Warsaw) 46 (2019), no. 1, 127-153.
  • [11] Z. Lerguet, M. Shillor and M. Sofonea, A frictional contact problem for an electro-viscoelastic body, Electron. J. Differential Equations 2007 (2007), Paper No. 170.
  • [12] Y. Li, S. A. Migórski and J. Han, A quasistatic frictional contact problem with damage involving viscoelastic materials with short memory, Math. Mech. Solids 21 (2016), no. 10, 1167-1183.
  • [13] S. A. Migórski, A. Ochal and M. Sofonea, Modeling and analysis of an antiplane piezoelectric contact problem, Math. Models Methods Appl. Sci. 19 (2009), no. 8, 1295-1324.
  • [14] J. Nec̃as and I. Hlavac̃ek, Mathematical Theory of Elastic and Elastoplastic Bodies: An Introduction, Elsevier, Amsterdam, 1981.
  • [15] P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Boston, 1985.
  • [16] V. Z. Patron and B. A. Kudryavtsev, Electromagnetoelasticity, Piezoelectrics and Electrically Conductive Solids, Gordon & Breach, London, 1988.
  • [17] M. Shillor, M. Sofonea and J. J. Telega, Models and Analysis of Quasistatic Contact, Springer, Berlin, 2004.
  • [18] M. Sofonea and E.-H. Essoufi, A piezoelectric contact problem with slip dependent coefficient of friction, Math. Model. Anal. 9 (2004), no. 3, 229-242.
  • [19] M. Sofonea, W. Han and M. Shillor, Analysis and Approximation of Contact Problems with Adhesion or Damage, Pure Appl. Math. (Boca Raton) 276, Chapman & Hall/CRC, Boca Raton, 2006.
  • [20] M. Sofonea, K. Kazmi, M. Barboteu and W. Han, Analysis and numerical solution of a piezoelectric frictional contact problem, Appl. Math. Model. 36 (2012), no. 9, 4483-4501.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-44b56f6e-25e3-41f1-af5d-25617513e132
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