Kluitenberg-Verh\'as rheology of solids in the GENERIC framework

Abstract

The internal variable methodology of nonequilibrium thermodynamics, with a symmetric tensorial internal variable, provides an important rheological model family for solids, the so-called Kluitenberg-Verh\'as model family [1]. This model family is distinguished not only from theoretical aspects but also on experimental grounds (see [2] for plastics and [3, 4, 5] for rocks). In this article, we present and discuss how the internal variable formulation of the Kluitenberg-Verh\'as model family can be presented in the nonequilibrium thermodynamical framework GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) [6, 7, 8, 9], for the benefit of both thermodynamical methodologies as well as for promising practical applications.