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Article

On the Second Law of Thermodynamics in Continuum Physics

1
Dipartimento di Ingegneria Civile Ambiente Territorio Architettura e Matematica, Università di Brescia, Via D. Valotti 9, 25133 Brescia, Italy
2
Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi, Università di Genova, Via All’Opera Pia 13, 16145 Genova, Italy
*
Author to whom correspondence should be addressed.
Thermo 2024, 4(2), 273-294; https://doi.org/10.3390/thermo4020015
Submission received: 16 May 2024 / Revised: 5 June 2024 / Accepted: 7 June 2024 / Published: 11 June 2024

Abstract

The paper revisits the formulation of the second law in continuum physics and investigates new methods of exploitation. Both the entropy flux and the entropy production are taken to be expressed by constitutive equations. In three-dimensional settings, vectors and tensors are in order and they occur through inner products in the inequality representing the second law; a representation formula, which is quite uncommon in the literature, produces the general solution whenever the sought equations are considered in rate-type forms. Next, the occurrence of the entropy production as a constitutive function is shown to produce a wider set of physically admissible models. Furthermore the constitutive property of the entropy production results in an additional, essential term in the evolution equation of rate-type materials, as is the case for Duhem-like hysteretic models. This feature of thermodynamically consistent hysteretic materials is exemplified for elastic–plastic materials. The representation formula is shown to allow more general non-local properties while the constitutive entropy production proves essential for the modeling of hysteresis.
Keywords: thermodynamic consistency; second law; exploitation of inequalities; rate equations; hysteresis thermodynamic consistency; second law; exploitation of inequalities; rate equations; hysteresis

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MDPI and ACS Style

Giorgi, C.; Morro, A. On the Second Law of Thermodynamics in Continuum Physics. Thermo 2024, 4, 273-294. https://doi.org/10.3390/thermo4020015

AMA Style

Giorgi C, Morro A. On the Second Law of Thermodynamics in Continuum Physics. Thermo. 2024; 4(2):273-294. https://doi.org/10.3390/thermo4020015

Chicago/Turabian Style

Giorgi, Claudio, and Angelo Morro. 2024. "On the Second Law of Thermodynamics in Continuum Physics" Thermo 4, no. 2: 273-294. https://doi.org/10.3390/thermo4020015

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