Abstract
Abstract The internal variable methodology of non-equilibrium thermodynamics, with a symmetric tensorial internal variable, provides an important rheological model family for solids, the so-called Kluitenberg–Verhás model family [Cs. Asszonyi et al., Contin. Mech. Thermodyn. 27, 2015]. This model family is distinguished not only by theoretical aspects but also on experimental grounds (see [Cs. Asszonyi et al., Period. Polytech., Civ. Eng. 60, 2016] for plastics and [W. Lin et al., Rock Engineering in Difficult Ground Conditions (Soft Rock and Karst), Proceedings of Eurock’09, 2009; K. Matsuki, K. Takeuchi, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30, 1993; K. Matsuki, Int. J. Rock Mech. Min. Sci. 45, 2008] for rocks). In this article, we present and discuss how the internal variable formulation of the Kluitenberg–Verhás model family can be presented in the non-equilibrium thermodynamical framework GENERIC (General Equation for the Non-Equilibrium Reversible–Irreversible Coupling) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, 2005; M. Grmela, J. Non-Newton. Fluid Mech. 165, 2010; M. Grmela, H. C. Öttinger, Phys. Rev. E 56, 1997; H. C. Öttinger, M. Grmela, Phys. Rev. E 56, 1997], for the benefit of both thermodynamical methodologies and promising practical applications.
Highlights
The internal variable approach of non-equilibrium thermodynamics, with a symmetric tensorial internal variable, provides a distinguished model family – the Kluitenberg–Verhás model family [1] – for the rheology of solids
We present and discuss how the internal variable formulation of the Kluitenberg–Verhás model family can be presented in the non-equilibrium thermodynamical framework GENERIC (General Equation for the NonEquilibrium Reversible–Irreversible Coupling) [H
Whenever a new non-equilibrium thermodynamical model emerges, it is advantageous and recommended to check how it suits the frame of GENERIC
Summary
The internal variable approach of non-equilibrium thermodynamics, with a symmetric tensorial internal variable, provides a distinguished model family – the Kluitenberg–Verhás model family [1] (covering the Hooke, Kelvin–Voigt, Maxwell, Poynting–Thomson, and Jeffrey models as special cases) – for the rheology of solids. This family is significant from a theoretical perspective and for experimental applications [2, 3, 4, 5].
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