Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory

Asszonyi, Csaba and Fülöp, Tamás and Ván, Péter (2015) Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory. CONTINUUM MECHANICS AND THERMODYNAMICS, 27 (6). pp. 971-986. ISSN 0935-1175

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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 pro- cesses 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 sug- gest to call the Kluitenberg–Verh´as 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–Verh´as 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.

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