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Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIThe Mechanics and Mathematics of Bodies Described by Implicit Constitutive Equations

Mathematical Analysis of Continuum Mechanics and Industrial Applications III: The Mechanics and... [In this short paper, I provide a brief discussion of the rationale and need for implicit constitutive relations for describing the response of many real materials. Classical theories to describe the response of materials such as the Cauchy theory of elasticity and the Navier–Stokes equations turn the demands of causality on its head and provide an expression for the Cauchy stress in terms of kinematical variables. It would be more reasonable instead to provide an expression for an appropriate kinematical variable in terms of the stress, if possible. However, in some instances such a specification might not be possible and we might have to resort to the prescription of an implicit relationship between the stress, its various frame-indifferent time derivatives, the appropriate kinematical variables and their frame-indifferent time derivative, as well as other relevant variables that influence the response of the body.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIThe Mechanics and Mathematics of Bodies Described by Implicit Constitutive Equations

Part of the Mathematics for Industry Book Series (volume 34)
Editors: Itou, Hiromichi; Hirano, Shiro; Kimura, Masato; Kovtunenko, Victor A.; Khludnev, Alexandr M.
Rajagopal, K. R.
Mathematical Analysis of Continuum Mechanics and Industrial Applications III — Aug 30, 2020
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Publisher
Springer Singapore
Copyright
© Springer Nature Singapore Pte Ltd. 2020
ISBN
978-981-15-6061-3
Pages
49 –65
DOI
10.1007/978-981-15-6062-0_4
Publisher site
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Abstract

[In this short paper, I provide a brief discussion of the rationale and need for implicit constitutive relations for describing the response of many real materials. Classical theories to describe the response of materials such as the Cauchy theory of elasticity and the Navier–Stokes equations turn the demands of causality on its head and provide an expression for the Cauchy stress in terms of kinematical variables. It would be more reasonable instead to provide an expression for an appropriate kinematical variable in terms of the stress, if possible. However, in some instances such a specification might not be possible and we might have to resort to the prescription of an implicit relationship between the stress, its various frame-indifferent time derivatives, the appropriate kinematical variables and their frame-indifferent time derivative, as well as other relevant variables that influence the response of the body.]

Published: Aug 30, 2020

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