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On non-equilibrium entropy in continuum thermodynamics of materials with memory

Huet C.

Archives of Mechanics

1999

Vol. 51, nr 2

123-154

Based on previous works of the author, the fundamentals of some basic concepts and methods currently used in the formulation of constitutive equations for linear or non-linear dissipative materials are revisited. The principles of the local state - or local equilibrium state - frequently used as the basis of Thermodynamics of Irreversible Processes in connection with the problem of the definition of a non-equilibrium entropy - are discussed, with emphasis laid on materials with memory exhibiting - as in linear or non-linear viscoelasticity - a delayed response to a constant loading. A adiabatic relaxation experiment is defined, from which it is shown that the usual formulation of the local state principle is too strong, since the set of relations which holds in equilibrium, and which makes use of macroscopic variables only, can never be applied without modification out of equilibrium. The same holds for the non-equilibrium Gibbs equation generally associated with the corresponding formalism when written with the real stress and temperature involved in the process. For dissipative behaviour of the differential type of order one, called also Markovian behaviour, a non-equilibrium entropy can be defined and some of the equilibrium relations can be applied to non-equilibrium situations. From this, a basic thermodynamic classification of rheological behaviour is obtained. In the non-Markovian case, the results are applied to the method of internal variables. A criterion for identifying suitable internal variables is obtained. They should correspond to Markovian behaviour when directly stimulated.