On the asymptotic behavior of solutions of anisotropic viscoelastic body

Abstract The quasistatic problem of a viscoelastic body in a three-dimensional thin domain with Tresca’s friction law is considered. The viscoelasticity coefficients and data for this system are assumed to vary with respect to the thickness ε. The asymptotic behavior of weak solution, when ε tends t...

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Autores principales:	Yassine Letoufa, Hamid Benseridi, Salah Boulaaras, Mourad Dilmi
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Anisotropy domain Asymptotic approach Viscoelastic body Quasistatic problem Tresca law Weak solution Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/40893079435747548d30cbbeadaa6573
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spelling	oai:doaj.org-article:40893079435747548d30cbbeadaa65732021-11-14T12:11:07ZOn the asymptotic behavior of solutions of anisotropic viscoelastic body10.1186/s13661-021-01567-w1687-2770https://doaj.org/article/40893079435747548d30cbbeadaa65732021-11-01T00:00:00Zhttps://doi.org/10.1186/s13661-021-01567-whttps://doaj.org/toc/1687-2770Abstract The quasistatic problem of a viscoelastic body in a three-dimensional thin domain with Tresca’s friction law is considered. The viscoelasticity coefficients and data for this system are assumed to vary with respect to the thickness ε. The asymptotic behavior of weak solution, when ε tends to zero, is proved, and the limit solution is identified in a new data system. We show that when the thin layer disappears, its traces form a new contact law between the rigid plane and the viscoelastic body. In which case, a generalized weak form equation is formulated, the uniqueness result for the limit problem is also proved.Yassine LetoufaHamid BenseridiSalah BoulaarasMourad DilmiSpringerOpenarticleAnisotropy domainAsymptotic approachViscoelastic bodyQuasistatic problemTresca lawWeak solutionAnalysisQA299.6-433ENBoundary Value Problems, Vol 2021, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Anisotropy domain Asymptotic approach Viscoelastic body Quasistatic problem Tresca law Weak solution Analysis QA299.6-433
spellingShingle	Anisotropy domain Asymptotic approach Viscoelastic body Quasistatic problem Tresca law Weak solution Analysis QA299.6-433 Yassine Letoufa Hamid Benseridi Salah Boulaaras Mourad Dilmi On the asymptotic behavior of solutions of anisotropic viscoelastic body
description	Abstract The quasistatic problem of a viscoelastic body in a three-dimensional thin domain with Tresca’s friction law is considered. The viscoelasticity coefficients and data for this system are assumed to vary with respect to the thickness ε. The asymptotic behavior of weak solution, when ε tends to zero, is proved, and the limit solution is identified in a new data system. We show that when the thin layer disappears, its traces form a new contact law between the rigid plane and the viscoelastic body. In which case, a generalized weak form equation is formulated, the uniqueness result for the limit problem is also proved.
format	article
author	Yassine Letoufa Hamid Benseridi Salah Boulaaras Mourad Dilmi
author_facet	Yassine Letoufa Hamid Benseridi Salah Boulaaras Mourad Dilmi
author_sort	Yassine Letoufa
title	On the asymptotic behavior of solutions of anisotropic viscoelastic body
title_short	On the asymptotic behavior of solutions of anisotropic viscoelastic body
title_full	On the asymptotic behavior of solutions of anisotropic viscoelastic body
title_fullStr	On the asymptotic behavior of solutions of anisotropic viscoelastic body
title_full_unstemmed	On the asymptotic behavior of solutions of anisotropic viscoelastic body
title_sort	on the asymptotic behavior of solutions of anisotropic viscoelastic body
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/40893079435747548d30cbbeadaa6573
work_keys_str_mv	AT yassineletoufa ontheasymptoticbehaviorofsolutionsofanisotropicviscoelasticbody AT hamidbenseridi ontheasymptoticbehaviorofsolutionsofanisotropicviscoelasticbody AT salahboulaaras ontheasymptoticbehaviorofsolutionsofanisotropicviscoelasticbody AT mouraddilmi ontheasymptoticbehaviorofsolutionsofanisotropicviscoelasticbody
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On the asymptotic behavior of solutions of anisotropic viscoelastic body

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