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2. Modeling of heat conduction through rate equations

Author

Giorgi, Claudio, Morro, Angelo, and Zullo, Federico

Subjects
Mathematical Physics
Abstract

Starting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. The statement of the Second Law is formulated in the classical form and the thermodynamic restrictions are then developed following the Coleman-Noll procedure. However, instead of the Clausius Duhem inequality we consider the corresponding equality where the entropy production rate is prescribed by a non-negative constitutive function. Both the free energy and the entropy production are assumed to depend on a common set of independent variables involving, in addition to temperature, both temperature gradient and heat-flux vector together with their time derivatives. This approach results in rate-type constitutive equations for the heat-flux vector that are intrinsically consistent with the Second Law and easily amenable to analysis. In addition to obtaining already known models (e.g. Cattaneo-Maxwell's, Jeffreys-like and Green-Naghdi's heat conductors), this scheme allows us to build new and more complex models of heat transport that may have applications in describing the thermal behavior in nanosystems. Indeed, when higher order time derivatives of the heat flux vector are involved, many different relaxation times occur within the rate equation., Comment: 32 pages, 2 tables, 1 appendix

Published
2024

5. Superconductivity and Superfluidity

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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6. Ferroics

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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7. Materials with Memory

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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8. Phase Transitions

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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9. Electromagnetism of Continuous Media

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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10. Mixtures

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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11. Plasticity

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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12. Micropolar Media

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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13. Rate-Type Models

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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14. Aging and Higher-Order Grade Materials

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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15. Porous Materials

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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16. Balance Equations

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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17. Solids

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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18. Generalities on Constitutive Models

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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19. Kinematics

Author

Morro, Angelo, Giorgi, Claudio, Bellomo, Nicola, Series Editor, Tezduyar, Tayfun E., Series Editor, Aoki, Kazuo, Editorial Board Member, Bazilevs, Yuri, Editorial Board Member, Chaplain, Mark, Editorial Board Member, Degond, Pierre, Editorial Board Member, Deutsch, Andreas, Editorial Board Member, Gibelli, Livio, Editorial Board Member, Herrero, Miguel Ángel, Editorial Board Member, Hughes, Thomas J.R., Editorial Board Member, Koumoutsakos, Petros, Editorial Board Member, Prosperetti, Andrea, Editorial Board Member, Rajagopal, K.R., Editorial Board Member, Takizawa, Kenji, Editorial Board Member, Tao, Youshan, Editorial Board Member, van Brummelen, Harald, Editorial Board Member, Morro, Angelo, and Giorgi, Claudio

Published
2023
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33. Solids

Author

Morro, Angelo, primary and Giorgi, Claudio, additional

Published
2023
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39. Strain-Rate and Stress-Rate Models of Nonlinear Viscoelastic Materials.

Author

Giorgi, Claudio and Morro, Angelo

Subjects
*DIFFERENTIAL forms, *VISCOELASTIC materials, *NONLINEAR equations, *ENTROPY, *EQUATIONS
Abstract

The paper is devoted to the modeling of nonlinear viscoelastic materials. The constitutive equations are considered in differential form via relations between strain, stress, and their derivatives in the Lagrangian description. The thermodynamic consistency is established by using the Clausius–Duhem inequality through a procedure that involves two uncommon features. Firstly, the entropy production is regarded as a positive-valued constitutive function per se. This view implies that the inequality is in fact an equation. Secondly, this statement of the second law is investigated by using an algebraic representation formula, thus arriving at quite general results for rate terms that are usually overlooked in thermodynamic analyses. Starting from strain-rate or stress-rate equations, the corresponding finite equations are derived. It then emerges that a greater generality of the constitutive equations of the classical models, such as those of Boltzmann and Maxwell, are obtained as special cases. [ABSTRACT FROM AUTHOR]

Published
2024
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