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Fluids 2018, 3(4), 69; https://doi.org/10.3390/fluids3040069

Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations

1
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8, CZ 186 75, Czech Republic
2
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Received: 3 September 2018 / Revised: 22 September 2018 / Accepted: 24 September 2018 / Published: 26 September 2018
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Abstract

Viscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives of second order, like those in Burgers’ model, are used to describe the complicated response of fluid like materials that are endowed with a complex microstructure that allows them to possess two different relaxation mechanisms as well as other non-Newtonian characteristics. Such models are used in geomechanics, biomechanics, chemical engineering and material sciences. We show how to develop such rate-type fluid models that include the classical Burgers’ model as well as variants of Burgers’ model, using a thermodynamic approach based on constitutive assumptions for two scalar quantities (namely, how the material stores energy and how the energy is dissipated) and appealing to the concept of natural configuration associated with the placement of the body that evolves as the body deforms. View Full-Text
Keywords: Burgers model; rate-type fluid models; viscoelasticity; second law of thermodynamics; thermodynamics Burgers model; rate-type fluid models; viscoelasticity; second law of thermodynamics; thermodynamics
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Málek, J.; Rajagopal, K.R.; Tůma, K. Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations. Fluids 2018, 3, 69.

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