Thermodynamically Consistent Evolution Equations in Continuum Mechanics
This paper addresses the modelling of material behaviour in terms of differential (or rate) equations. To comply with the objectivity principle, recourse is made to invariant fields in the Lagrangian description or to objective time derivatives in the Eulerian description. The thermodynamic consiste...
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2024-10-01
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| author | Angelo Morro |
| author_facet | Angelo Morro |
| author_sort | Angelo Morro |
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| description | This paper addresses the modelling of material behaviour in terms of differential (or rate) equations. To comply with the objectivity principle, recourse is made to invariant fields in the Lagrangian description or to objective time derivatives in the Eulerian description. The thermodynamic consistency is investigated in terms of the Clausius–Duhem inequality with two unusual features. Firstly, the (non-negative) entropy production is viewed as a constitutive function per se. Secondly, the inequality is viewed as a constraint on the pertinent fields and it is solved by using a representation formula, which allows for the the admissibility of a class of models. For definiteness, models of heat conduction are established, within Lagrangian descriptions, while models of the Navier–Stokes–Voigt fluid are investigated within Eulerian descriptions. In connection with thermo-viscous fluids, evolution equations are investigated within the Eulerian description. It is shown that the thermodynamic consistency is compatible with both objective and non-objective evolution equations. |
| format | Article |
| id | doaj-art-af220ca68a4544e2a46304a0f00425d2 |
| institution | Kabale University |
| issn | 2673-9321 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Foundations |
| spelling | doaj-art-af220ca68a4544e2a46304a0f00425d22024-12-27T14:26:55ZengMDPI AGFoundations2673-93212024-10-014449451210.3390/foundations4040033Thermodynamically Consistent Evolution Equations in Continuum MechanicsAngelo Morro0Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi, Università di Genova, 16145 Genova, ItalyThis paper addresses the modelling of material behaviour in terms of differential (or rate) equations. To comply with the objectivity principle, recourse is made to invariant fields in the Lagrangian description or to objective time derivatives in the Eulerian description. The thermodynamic consistency is investigated in terms of the Clausius–Duhem inequality with two unusual features. Firstly, the (non-negative) entropy production is viewed as a constitutive function per se. Secondly, the inequality is viewed as a constraint on the pertinent fields and it is solved by using a representation formula, which allows for the the admissibility of a class of models. For definiteness, models of heat conduction are established, within Lagrangian descriptions, while models of the Navier–Stokes–Voigt fluid are investigated within Eulerian descriptions. In connection with thermo-viscous fluids, evolution equations are investigated within the Eulerian description. It is shown that the thermodynamic consistency is compatible with both objective and non-objective evolution equations.https://www.mdpi.com/2673-9321/4/4/33models of continuathermodynamic consistencyobjectivityentropy production |
| spellingShingle | Angelo Morro Thermodynamically Consistent Evolution Equations in Continuum Mechanics Foundations models of continua thermodynamic consistency objectivity entropy production |
| title | Thermodynamically Consistent Evolution Equations in Continuum Mechanics |
| title_full | Thermodynamically Consistent Evolution Equations in Continuum Mechanics |
| title_fullStr | Thermodynamically Consistent Evolution Equations in Continuum Mechanics |
| title_full_unstemmed | Thermodynamically Consistent Evolution Equations in Continuum Mechanics |
| title_short | Thermodynamically Consistent Evolution Equations in Continuum Mechanics |
| title_sort | thermodynamically consistent evolution equations in continuum mechanics |
| topic | models of continua thermodynamic consistency objectivity entropy production |
| url | https://www.mdpi.com/2673-9321/4/4/33 |
| work_keys_str_mv | AT angelomorro thermodynamicallyconsistentevolutionequationsincontinuummechanics |