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Sull’espressione analitica di alcune grandezze termodinamiche nei materiali con memoria. (English) Zbl 0535.73029
For linear viscoelastic materials and for (spacewise) one-dimensional processes at constant temperature the author compares the expression of the free energy proposed earlier by himself [Ann. Math. Pura Appl., IV. Ser. 98, 273-279 (1974; Zbl 0281.73027)] with one suggested by B. Coleman [Arch. Ration. Mech. Anal. 17, 1-46 (1964)] and by W. A. Day [The thermodynamics of simple materials with memory (1972; Zbl 0295.73007)] (for the case when the relaxation function is of exponential type). He finds that (interpreted also for more general types of relaxation functions) the expression of Day and Coleman appears to have more strict extremum properties, but, unfortunately, does not always assure the verification of the Clausius-Duhem inequality.
Reviewer: G.Capriz

MSC:
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74A15 Thermodynamics in solid mechanics
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
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References:
[1] B. Coleman , Thermodynamics of Materials with Memory , Archive for Rational Mechanics and Analysis , XVII ( 1964 ), pp. 1 - 46 . MR 171419 | Zbl 0286.73006 · Zbl 0286.73006
[2] C. Truesdell , Rational Mechanics , Mc. Graw-Hill , New York , 1969 . (Traduzione italiana di M. Fichera Colautti , Contributi del Centro Linceo , n. 20 , Accademia Nazionale dei Lincei , Roma , 1976 ).
[3] W.A. Day , The Thermodynamics of Simple Materials with Fading Memory , Springer - Verlag - Berlin , Heidelberg , New York ( 1972 ). MR 366234 | Zbl 0295.73007 · Zbl 0295.73007
[4] W.A. Day , The Thermodynamics of Materials with Memory , Liguori Napoli ( 1979 ), pp. 55 - 91 . Zbl 0465.73004 · Zbl 0465.73004
[5] D. Graffi , Sull’espressione dell’energia libera nei materiali visco-elastici lineari , Annali di Matematica Pura e Applicata ( IV ), XCVIII , pp. 273 - 279 . MR 345497 | Zbl 0281.73027 · Zbl 0281.73027
[6] D. Graffi , Qualche problema di elettromagnetismo, Trends in Applications of Pure Mathematics to Mechanics , edited by G. FICHERA- Pitman , London , 1976 , pp. 129 - 144 . MR 484021 | Zbl 0357.35073 · Zbl 0357.35073
[7] B. Coleman - V. Mizel , On the stability of solutions of functional differential equations , Archive of Rational Mechanics and Analysis , XXX ( 1968 ), pp. 173 - 196 . MR 229933 | Zbl 0184.36801 · Zbl 0184.36801
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