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Keywords = extended Coleman–Noll procedure

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16 pages, 287 KiB  
Article
Heat-Flux Relaxation and the Possibility of Spatial Interactions in Higher-Grade Materials
by Vito Antonio Cimmelli
Mathematics 2025, 13(4), 599; https://doi.org/10.3390/math13040599 - 12 Feb 2025
Viewed by 612
Abstract
We investigate the thermodynamic compatibility of weakly nonlocal materials with constitutive equations depending on the third spatial gradient of the deformation and the heat flux ruled by an independent balance law. In such materials, the molecules experience long-range interactions. Examples of biological systems [...] Read more.
We investigate the thermodynamic compatibility of weakly nonlocal materials with constitutive equations depending on the third spatial gradient of the deformation and the heat flux ruled by an independent balance law. In such materials, the molecules experience long-range interactions. Examples of biological systems undergoing nonlocal interactions are given. Under the hypothesis of weak nonlocality (constitutive equations depending on the gradients of the unknown fields), we exploit the second law of thermodynamics by considering the spatial differential consequences (gradients) of the balance laws as additional equations to be substituted into the entropy inequality, up to the order of the gradients entering the state space. As a consequence of such a procedure, we obtain generalized constitutive laws for the stress tensor and the specific entropy, as well as new forms of the balance equations. Such equations are, in general, parabolic, although hyperbolic situations are also possible. For small deformations of homogeneous and isotropic bodies, under the validity of a generalized Maxwell–Cattaneo equation for the heat flux, which depends on the deformation too, we study the propagation of small-amplitude thermomechanical waves, proving that mechanical, thermal and thermomechanical waves are possible. Full article
18 pages, 324 KiB  
Article
Interpretation of Second Law of Thermodynamics in Extended Procedures for the Exploitation of the Entropy Inequality: Korteweg Fluids and Strain-Gradient Elasticity as Examples
by Vito Antonio Cimmelli
Entropy 2024, 26(4), 293; https://doi.org/10.3390/e26040293 - 27 Mar 2024
Cited by 1 | Viewed by 1109
Abstract
In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the [...] Read more.
In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the assumption that, at an arbitrary instant, t0, in an arbitrary point, P0, of a continuous system, the entropy production is zero if, and only if, P0 is in thermodynamic equilibrium. In 2022, Cimmelli and Rogolino incorporated such an assumption in a more general formulation of the second law of thermodynamics. In this paper, we prove that the same conclusions hold if both the fundamental balance laws and their gradients are substituted into the entropy inequality. Such a methodology is applied to analyze the strain-gradient elasticity. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
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