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.

Szarka (1927Szarka ( -2015. Keywords IntroductionMotivated by problems in rock mechanics and similar challenges in the continuum theory of solids, in the last few years, our research object has been to achieve an amalgamation of a new approach [1][2][3][4] to the problem of objectivity and of material frame indifference -based on Matolcsi's framework [5-8] -with a recent activity in nonequilibrium thermodynamics [9][10][11][12] that focuses on the role of thermodynamical stability and on a constructive quantitative exploitation of the content of the second law of thermodynamics. Here, we present how this program has accomplished a theoretical framework for the continuum thermo-elasto-visco-plasto-mechanics of solids.Accordingly, the aspects covered currently are: • elasticity, an immediate response to mechanical loading, and during which mechanical energy is conserved; • rheology, which, in contrast, is a delayed response, with mechanical energy partially dissipated, and which may be attributed to viscous damping, for instance; • plasticity, which is permanent shape change caused by mechanical loading: a change of the unloaded shape; • thermal expansion, and the thermal stress generated by it;• and heat conduction. In parallel to the general level -large deformation theory, general constitutive equations -, we consider it inevitable to exhibit (and countercheck!) the applicability of the formulation to practical concrete examples. To this end, we have performed experiments on which the theory can be applied and tested. The experimental results presented here illustrate the various predictions of the theory both qualitatively and quantitatively. Via this simple yet widely informative and insightful experimental example -mechanical and thermal monitoring of uniaxial stretching of polyamide-6 plastic samples -, the various thermomechanical effects in solids are well demonstrated and the correspondence to the theoretical expectations are satisfactorily established.Therefore, though the theoretical framework described here is capable to describe completely general situations, here our aim is to focus on the connection between theory and experiment so, at each component of our theoretical formulation, we take the simplest applicable concrete choice: small deforma-