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

TL;DR

This paper develops a thermodynamical rheological model called the Kluitenberg-Verhás body, extending classical models with internal variables and inertial effects, ensuring thermodynamic consistency and parameter restrictions.

Contribution

It introduces a unified thermodynamical framework for rheology using internal variables, extending existing models with new restrictions and insights.

Findings

The model generalizes the Jeffreys model to solids.

Parameter restrictions ensure thermodynamic consistency.

Comparison with other thermodynamical approaches highlights its universality.

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-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.