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

Sengul, Yasemin 2021. One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity. Applications in Engineering Science 7 , 100058. 10.1016/j.apples.2021.100058

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Abstract

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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Additional Information: This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
ISSN: 2666-4968
Date of First Compliant Deposit: 29 November 2021
Date of Acceptance: 11 June 2021
Last Modified: 29 Nov 2021 12:20
URI: https://orca.cardiff.ac.uk/id/eprint/145682

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