Distinguished rheological models 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 words, is the extension of Jeffreys model to solids. We argue that this Kluitenberg-Verhás body is the natural thermodynamical building block of rheology. An important feature of the presented methodology is that nontrivial inequality-type restrictions arise for the four parameters of the model. We compare these conditions and other aspects to those of other known thermodynamical approaches, like Extended Irreversible Thermodynamics or the original theory of Kluitenberg.

16 pages, 1 figure, revised

References in corpus (1)

• Universal heat conduction -- the thermodynamics of some weakly nonlocal theories

Cited by in corpus (11)

• Generalized ballistic-conductive heat conduction in isotropic materials
• Thermodynamical extension of a symplectic numerical scheme with half space and time shift demonstrated on rheological waves in solids
• Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics
• Four spacetime dimensional simulation of rheological waves in solids and the merits of thermodynamics
• Long term measurements from the Mátra Gravitational and Geophysical Laboratory
• First report of long term measurements of the {MGGL} laboratory in the {M}átra mountain range
• Kluitenberg-Verhás rheology of solids in the GENERIC framework
• Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids
• A case study of non-Fourier heat conduction using Internal Variables and GENERIC
• Thermodynamic aspects of rock friction
• Continuum modeling perspectives of non-Fourier heat conduction in biological systems