One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity

In this note a one-dimensional nonlinear partial differential equation, which has been recently introduced by the author and co-workers, describing the response of viscoelastic solids showing limiting strain behaviour in strain and stress-rate cases is investigated. The model results from an implici...

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Autor principal:	Yasemin Şengül
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	35A99 35R15 35Q72 74A20 74B20 74D10 Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/aa15de92511a429d8790d08a99487efb
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spelling	oai:doaj.org-article:aa15de92511a429d8790d08a99487efb2021-12-01T05:06:17ZOne-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity2666-496810.1016/j.apples.2021.100058https://doaj.org/article/aa15de92511a429d8790d08a99487efb2021-09-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496821000248https://doaj.org/toc/2666-4968In this note a one-dimensional nonlinear partial differential equation, which has been recently introduced by the author and co-workers, describing the response of viscoelastic solids showing limiting strain behaviour in strain and stress-rate cases is investigated. The model results from an implicit constitutive relation between the linearized strain and the stress. For this viscoelastic model, a specific form of the nonlinearity that has been investigated only in the elastic case in the literature is studied and it is shown that traveling wave solutions can be found analytically or numerically for various approximations of the nonlinearity, as well as the nonlinearity itself. Moreover, the analysis is carried out for both small and larger values of the stress, the latter being the first time in the literature within the current context.Yasemin ŞengülElsevierarticle35A9935R1535Q7274A2074B2074D10Engineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 7, Iss , Pp 100058- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	35A99 35R15 35Q72 74A20 74B20 74D10 Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	35A99 35R15 35Q72 74A20 74B20 74D10 Engineering (General). Civil engineering (General) TA1-2040 Yasemin Şengül One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity
description	In this note a one-dimensional nonlinear partial differential equation, which has been recently introduced by the author and co-workers, describing the response of viscoelastic solids showing limiting strain behaviour in strain and stress-rate cases is investigated. The model results from an implicit constitutive relation between the linearized strain and the stress. For this viscoelastic model, a specific form of the nonlinearity that has been investigated only in the elastic case in the literature is studied and it is shown that traveling wave solutions can be found analytically or numerically for various approximations of the nonlinearity, as well as the nonlinearity itself. Moreover, the analysis is carried out for both small and larger values of the stress, the latter being the first time in the literature within the current context.
format	article
author	Yasemin Şengül
author_facet	Yasemin Şengül
author_sort	Yasemin Şengül
title	One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity
title_short	One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity
title_full	One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity
title_fullStr	One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity
title_full_unstemmed	One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity
title_sort	one-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/aa15de92511a429d8790d08a99487efb
work_keys_str_mv	AT yaseminsengul onedimensionalstrainlimitingviscoelasticitywithanarctangenttypenonlinearity
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One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity

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