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

Şengül Tezel, Yasemin (2021) One-dimensional strain-limiting viscoelasticity with an arctangent type nonlinearity. Applications in Engineering Science, 7 . ISSN 2666-4968

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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
Uncontrolled Keywords: Semilinear equations; Strain-limiting theory; Traveling wave; Traveling waves; Viscoelasticity
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Yasemin Şengül Tezel
Date Deposited: 04 Sep 2022 18:19
Last Modified: 04 Sep 2022 18:19

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