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Nonlinear viscoelasticity of strain rate type: an overview

Şengül Tezel, Yasemin (2021) Nonlinear viscoelasticity of strain rate type: an overview. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2245). ISSN 1364-5021 (Print) 1471-2946 (Online)

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Official URL: http://dx.doi.org/10.1098/rspa.2020.0715

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
Additional Information:WoS Document Type: Review
Uncontrolled Keywords:viscoelasticity; solid mechanics; nonlinear partial differential equations
Subjects:Q Science > QA Mathematics > QA299.6-433 Analysis
Q Science > QA Mathematics
ID Code:41351
Deposited By:Yasemin Şengül Tezel
Deposited On:11 Mar 2021 16:57
Last Modified:11 Mar 2021 16:57

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