Heat-Flux Relaxation and the Possibility of Spatial Interactions in Higher-Grade Materials

Vito Antonio Cimmelli ()
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Vito Antonio Cimmelli: Department of Fundamental and Applied Sciences, University of Basilicata, Via dell’Ateneo Lucano, 10, 85100 Potenza, Italy

Mathematics, 2025, vol. 13, issue 4, 1-16

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 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.

Keywords: thermoviscoelastic solids; weakly nonlocal constitutive equations; heat-flux relaxation; extended Coleman–Noll procedure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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