Classical results for a non-classical theory: Remarks on thermodynamic relations in Green-Naghdi thermo-hyperelasticity

Bargmann, S. and Steinmann, P. (2007) Classical results for a non-classical theory: Remarks on thermodynamic relations in Green-Naghdi thermo-hyperelasticity. Continuum Mechanics and Thermodynamics, 19(1-2), pp. 59-66. (doi: 10.1007/s00161-007-0045-x)

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Abstract

In this contribution we first investigate the thermodynamic’s relation between the entropy flux H and the heat flux Q in the non-classical theory of Green and Naghdi imposed by the entropy equality used in their approach. We show that the classical assumption entropy flux = heat flux/absolute temperature holds for isotropic materials by exploiting the entropy principle of Müller and Liu. As opposed to the usual procedure, we formulate the balance laws with respect to the material description. Subsequently, further restrictions are obtained by exploiting the entropy principle as suggested by Green and Naghdi (in Proc. R. Soc. Lond. 432, 171–194, 1991). This yields the classical potential relations between the entropy and the free energy and between the second Piola-Kirchhoff stress tensor and the free energy.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Bargmann, S., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Continuum Mechanics and Thermodynamics
Publisher:Springer
ISSN:0935-1175
ISSN (Online):1432-0959
Published Online:08 May 2007

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