2014
DOI: 10.1007/s00161-014-0392-3
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Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory

Abstract: We present and analyze a thermodynamical theory of rheology with single internal variable. The universality of the model is ensured as long as the mesoscopic and/or microscopic background processes satisfy the applied thermodynamical principles, which are the second law, the basic balances and the existence of an additional-tensorial-state variable. The resulting model, which we suggest to call the Kluitenberg-Verhás body, is the Poynting-Thomson-Zener body with an additional inertial element, or, in other wor… Show more

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Cited by 36 publications
(33 citation statements)
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“…In this paper mostly the results of Hungarian Miocene limestone [10] British sandstones [2,3,9] and rhyolitic tuffs from Eger (Hungary) [4] were analyzed, but similar results were found for other Hungarian tuffs [30] and these results can be used in general [31]. Notably, for a more precise and fundamental description of the mechanical behavior of rock, one should apply non-equilibrium continuum thermodynamics along the lines of [36,37] and beyond. The similarity of the regression lines for the different rock types was unexpected from a theoretical point of view, although it is of note that a similar relationship has been reported as a consequence of damage related thermodynamic stability [38,39].…”
Section: Discussionmentioning
confidence: 88%
“…In this paper mostly the results of Hungarian Miocene limestone [10] British sandstones [2,3,9] and rhyolitic tuffs from Eger (Hungary) [4] were analyzed, but similar results were found for other Hungarian tuffs [30] and these results can be used in general [31]. Notably, for a more precise and fundamental description of the mechanical behavior of rock, one should apply non-equilibrium continuum thermodynamics along the lines of [36,37] and beyond. The similarity of the regression lines for the different rock types was unexpected from a theoretical point of view, although it is of note that a similar relationship has been reported as a consequence of damage related thermodynamic stability [38,39].…”
Section: Discussionmentioning
confidence: 88%
“…for simplicity), (2) is the kinematic relationship between the strain field ε 3 and v, and the rheological relationship (3) contains, in addition to Young's modulus E, two positive coefficientsÊ, τ. The Poynting-Thomson-Zener model is a subfamily within the Kluitenberg-Verhás model family, which family can be obtained via a nonequilibrium thermodynamical internal variable approach [16]. The Poynting-Thomson-Zener model looks particularly simple, after eliminating the internal variable, both in specific energy e total and in specific entropy s:…”
Section: Properties Of the Continuum Modelmentioning
confidence: 99%
“…There are several models leading to horizontal S-curves for the stress-strain dependency (multiple shear rates for a single shear stress). For instance, the Johnson-Segalman model [33] or rather its weakly non-local variant [47], thermodynamics with internal variables [68,2], viscoelastic models undergoing scission of polymeric chains [26] or viscoelastic models with relaxation of internal structure [59,21] indicate the horizontal S-shape of the stress-strain relation. The literature is rather vast, and we do not attempt to make the list of references complete.…”
Section: Shear and Vorticity Bandingmentioning
confidence: 99%