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Modelling of elastic heat conductors via objective rate equations

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Abstract

A thermoelastic solid is modelled by letting the heat flux be given by a rate equation. As any constitutive property, the rate equation has to be objective and consistent with thermodynamics. Accordingly, firstly a theorem is given that characterizes objective time derivatives. This allows the known objective time derivatives to be viewed as particular elements of the set so specified. Next the thermodynamic consistency is established for the constitutive models involving objective time derivatives within appropriate sets. It emerges that the thermodynamic consistency holds provided the stress contains additively terms quadratic in the heat flux vector in a form that is related to the derivative adopted for the rate of the heat flux.

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Acknowledgements

Preliminary results on this topic were delivered at JETC 2017, Budapest. The author is grateful to the reviewers for constructive criticism on the objectivity principle.

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Authors and Affiliations

  1. DIBRIS, University of Genoa, Via Opera Pia 13, 16145, Genoa, Italy

    Angelo Morro

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  1. Angelo Morro
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Correspondence to Angelo Morro.

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Communicated by Attila R. Imre.

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Morro, A. Modelling of elastic heat conductors via objective rate equations. Continuum Mech. Thermodyn. 30, 1231–1243 (2018). https://doi.org/10.1007/s00161-017-0617-3

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