The DNLR approach and relaxation phenomena. Part I - Historical account and DNLR formalism

The relaxation phenomena defined by De Groot and Mazur (1962) describe the internal reorganizations linked to the return to equilibrium of media subjected to external perturbations of low amplitude (near the equilibrium state). Far from equilibrium, any theoretical approach to these phenomena has to include the following information: the internal reorganizations are multiple and their kinetics are nonlinear. Indeed, much experimental evidence has lead to this conclusion. A classical example for the analysis of relaxations near the glass transition is the experimental study of the volume recovery of PVAc (Polyvinylacetate) done by Kovacs (1963). Over many years, we have developed an approach in the framework of irreversible thermodynamics, called the Distribution of Non-Linear Relaxations (DNLR) to establish constitutive laws for various materials under coupled physical solicitations. It is based on a generalization of the fundamental Gibbs equation (1902) for systems outside equilibrium. This relation combines the two laws of thermodynamics into a single expression; for example, the internal energy e = e(s, v, n(i),...) depends on the whole of the state variables, including the entropy s. The salient points of the DNLR approach are (i) to naturally take account of the couplings found in physics, (ii) the multiplicity of the mechanisms of internal reorganization and (iii) the nonlinearity of the kinetics for the return to equilibrium. The aim of this paper is then (i) to present in this first part the bases, the formalism, and the framework of the DNLR approach and (ii) in a second part to check the pertinence of this general DNLR strategy to simulate the experimental data of Kovacs concerning PVAc. This developed modeling will be compared to other works already done in the literature.