Sezione F7 Meccanica del continuo

Minimum free energy in heat conduction:
materials with memory 1
Sandra Carillo
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di
Roma “La Sapienza”, I-00161 Rome, Italy
The minimum free energy is obtained in the cases of a rigid linear heat conductor with
memory. Thus, the result is compared with results concerning the minimum free energy
in isothermal viscoelasticity. Interesting similarities can be observed when such results
are compared. In addition, in both the cases, the minimum free energy is related to
the maximum recoverable work. The model of rigid heat conductor here adopted is that
one comprised in Fabrizio, Gentili and Reynolds [3] where the thermodynamics of a rigid
omogeneous linear heat conductor with memory is studied. The results concerning the
minimum free energy in this framework have been recently studied [1]; they are compared
with results in the study of isothermal viscoelasticity. In particular, results here referred
to have been obtained by Fabrizio and Golden [4], Fabrizio, Deseri, Gentili and Golden
[2], Golden [6], Gentili [5], where, in addition, historical notes as well as many references
on the study of isothermal viscoelasticity are comprised.
E-mail address: carillo@dmmm.uniroma1.it
References
[1] S. Carillo: A rigid linear heat conductor with memory: minimum free energy, preprint
Dipartimento di Metodi e Modelli Matematici, Universita‘ di Roma “La Sapienza”,
2003.
[2] L. Deseri, G. Gentili, J.M. Golden: An Explicit Formula for the Minimum Free Energies
in Linear Viscoelasticity, J. Elasticity, 54, p. 141-185, 1999.
[3] M. Fabrizio, G. Gentili, D.W.Reynolds: On rigid heat conductors with memory, Int.
J. Eng. Sci. , 36, p. 765–782, 1998.
[4] M. Fabrizio, J.M. Golden: Maximum and minimum free energies for a linear viscoelastic
material, Quart. Appl. Math., 60, no. 2, p. 341–381, 2002.
[5] G. Gentili: Maximum recoverable work, minimum free energy and state space in linear
viscoelasticity, Quart. Appl. Math., 60, no. 1, p. 153–182, 2002.
[6] J. M. Golden: Free energies in the frequency domain: the scalar case, Quart. Appl.
Math., 58, p. 121–150, 2000.
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Classificazione AMS 80A20, 74F05
Under the support of G.N.F.M.-I.N.D.A.M. and of M.I.U.R., Progetto Cofinanziato 2002 Modelli Matematici
per la Scienza dei Materiali
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