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Nonlinear viscoelasticity of strain rate type: an overview

Sengul, Yasemin 2021. Nonlinear viscoelasticity of strain rate type: an overview. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477 (2245) , 20200715. 10.1098/rspa.2020.0715

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Abstract

There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a class of viscoelastic solids. In particular, nonlinear viscoelasticity of strain rate type, which can be described by a constitutive relation for the stress function depending not only on the strain but also on the strain rate, is considered. This particular case is not only favourable from a mathematical analysis point of view but also due to experimental observations, knowledge of the strain rate sensitivity of viscoelastic properties is crucial for accurate predictions of the mechanical behaviour of solids in different areas of applications. First, a brief introduction of some basic terminology and preliminaries, including kinematics, material frame-indifference and thermodynamics, is given. Then, considering the governing equations with constitutive relationships between the stress and the strain for the modelling of nonlinear viscoelasticity of strain rate type, the most general model of interest is obtained. Then, the long-term behaviour of solutions is discussed. Finally, some applications of the model are presented.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: The Royal Society
ISSN: 1364-5021
Date of First Compliant Deposit: 3 November 2021
Date of Acceptance: 18 December 2020
Last Modified: 05 Nov 2021 09:28
URI: https://orca.cardiff.ac.uk/id/eprint/145140

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