Variational Inequality Models Arising in the Study of Viscoelastic Materials

Oanh Chau (), Daniel Goeleven () and Rachid Oujja ()
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Oanh Chau: University of La Réunion
Daniel Goeleven: University of La Réunion
Rachid Oujja: University of La Réunion

A chapter in Optimization in Science and Engineering, 2014, pp 33-66 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(6):635–648, 2004; Addi et al., Discrete Continuous Dyn. Syst. 31(4):1039–1051, 2011; Adly et al., Numer. Algebra Control Optim. 2(1):89–101, 2012; Adly and Chau, Math. Program. Ser. B, 2014; 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; Contact Problem; Maximal Monotone; Real Hilbert Space; Frictional Contact (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0808-0_2

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DOI: 10.1007/978-1-4939-0808-0_2

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