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The derivation of constitutive relations from the free energy and the dissipation function. (English) Zbl 0719.73001
The field between (continuum) mechanics and thermodynamics appears to have some of the characteristics of that indistinct country one reads about in novels, which separates (or used to separate) the German/Austrian world from the Russian empire. Flat or slightly hilly, marshy or with forests of birches one got easily lost in, and (except for a few well known and well trodden highways) hardly connected to the west with the rigorous teutonic milieu and opening up to the east towards imense wastes. Few the safe routes through the quicksand or the dark wood; many the smart guides offering help in getting across.
One way out of the nightmare is to accept the strategy long proposed by Professor Ziegler [H. Ziegler, An introduction to thermomechanics (1983; Zbl 0531.73080)] and expounded by him also in a book on thermodynamics: an orthogonality principle for irreversible processes, based on a dissipation function and including Onsager’s theory as a special case. The present paper gives a systematic account of the leading functions providing constitutive relations. A brief aperçu of the theory opens the paper; the rest of the article is devoted to applications, almost invariably successful, in an impressive variety of cases.
Reviewer: G.Capriz (Pisa)

74A20 Theory of constitutive functions in solid mechanics
74A15 Thermodynamics in solid mechanics
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