Variational Inequality Models Arising in the Study of Viscoelastic Materials

O. Chau (), D. Goeleven () and R. Oujja ()
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O. Chau: University of La Réunion, PIMENT EA4518
D. Goeleven: University of La Réunion, PIMENT EA4518
R. Oujja: University of La Réunion, PIMENT EA4518

A chapter in Mathematics Without Boundaries, 2014, pp 93-126 from Springer

Abstract: 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.

Keywords: Variational inequality; Evolution inequality; Fixed point; Weak solutions; Dynamic process; Friction; Thermo-viscoelasticity; Subdifferential contact condition; Nonclamped condition; Numerical analysis; Numerical simulations (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1106-6_4

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DOI: 10.1007/978-1-4939-1106-6_4

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