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Traveling waves in one-dimensional non-linear models of strain-limiting viscoelasticity

Erbay, H. A. and Sengul, Yasemin 2015. Traveling waves in one-dimensional non-linear models of strain-limiting viscoelasticity. International Journal of Non-Linear Mechanics 77 , pp. 61-68. 10.1016/j.ijnonlinmec.2015.07.005

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In this paper we investigate traveling wave solutions of a non-linear differential equation describing the behaviour of one-dimensional viscoelastic medium with implicit constitutive relations. We focus on a subclass of such models known as the strain-limiting models introduced by Rajagopal. To describe the response of viscoelastic solids we assume a non-linear relationship among the linearized strain, the strain rate and the Cauchy stress. We then concentrate on traveling wave solutions that correspond to the heteroclinic connections between the two constant states. We establish conditions for the existence of such solutions, and find those solutions, explicitly, implicitly or numerically, for various forms of the non-linear constitutive relation.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0020-7462
Date of Acceptance: 15 July 2015
Last Modified: 25 Nov 2021 13:57

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