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The DNLR Approach and Relaxation Phenomena. Part I – Historical Account and DNLR Formalism

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Abstract

The relaxation phenomena defined by De Groot and Mazur (1962)describe the internal reorganizations linked to the return toequilibrium of media subjected to external perturbations of lowamplitude (near the equilibrium state). Far from equilibrium, anytheoretical approach to these phenomena has to include the followinginformation: the internal reorganizations are multiple and theirkinetics are nonlinear. Indeed, much experimental evidence has lead tothis conclusion. A classical example for the analysis of relaxationsnear the glass transition is the experimental study of the volumerecovery of PVAc (Polyvinylacetate) done by Kovacs (1963).

Over many years, we have developed an approach in the framework ofirreversible thermodynamics, called the Distribution of Non-LinearRelaxations (DNLR) to establish constitutive laws for various materialsunder coupled physical solicitations. It is based on a generalization ofthe fundamental Gibbs equation (1902) for systems outside equilibrium.This relation combines the two laws of thermodynamics into a singleexpression; for example, the internal energy e =e(s, v, n i , ¨)depends on the whole of the state variables, including theentropy s. The salient points of the DNLR approach are (i)to naturally take account of the couplings found in physics, (ii) themultiplicity of the mechanisms of internal reorganization and (iii) thenonlinearity of the kinetics for the return to equilibrium.

The aim of this paper is then (i) to present in this first part thebases, the formalism, and the framework of the DNLR approach and (ii) ina second part to check the pertinence of this general DNLR strategy tosimulate the experimental data of Kovacs concerning PVAc. This developedmodeling will be compared to other works already done in the literature.

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  1. LEMTA, UMR CNRS 7563, ENSEM—INPL, B.P. 160, 2 Av. de La Fôret de Haye, F-54504, Vandoeuvre lès Nancy, France

    Christian Cunat

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Cunat, C. The DNLR Approach and Relaxation Phenomena. Part I – Historical Account and DNLR Formalism. Mechanics of Time-Dependent Materials 5, 39–65 (2001). https://doi.org/10.1023/A:1009899519935

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