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Variational Inequality Models Arising in the Study of Viscoelastic Materials

In: Mathematics Without Boundaries

Author

Listed:
  • O. Chau

    (University of La Réunion, PIMENT EA4518)

  • D. Goeleven

    (University of La Réunion, PIMENT EA4518)

  • R. Oujja

    (University of La Réunion, PIMENT EA4518)

Abstract

In this paper, we present a synthesis of different results obtained recently in the papers (Chau and Awbi, Appl Anal 83:635–648, 2004; Addi et al. Discret Contin Dyn Syst 31:1039–1051, 2011; Adly et al. Numer Algebra Control Optim 2:89–101, 2012; Adly and chau, to appear in Mathematical Programming; Chau et al., Int J Appl Math Mech, 2012). It concerns the study of contact problems for viscoelastic materials with possible thermal effects. We first describe a general thermo-viscoelastic model involving a thermo-viscoelastic Kelvin–Voigt constitutive law, a temperature field governed by the heat equation and a subdifferential surface contact condition. Then, we study a model which describes the frictional contact between a short memory thermo-viscoelastic body and a given rigid foundation. The free boundary contact problem for a long memory viscoelastic material is also considered. Finally, we provide numerical simulations for different fundamental examples of thermal contact problems.

Suggested Citation

  • O. Chau & D. Goeleven & R. Oujja, 2014. "Variational Inequality Models Arising in the Study of Viscoelastic Materials," Springer Books, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Mathematics Without Boundaries, edition 127, pages 93-126, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1106-6_4
    DOI: 10.1007/978-1-4939-1106-6_4
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