Free energy and internal variables in linear viscoelasticity

Angelo Morro; Maurizio Vianello

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1989)

  • Volume: 83, Issue: 1, page 215-219
  • ISSN: 0392-7881

Abstract

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In connection with the determination of the free energy functional for the viscoelastic stress tensor, a viscoelastic material is considered as described by a material with internal variables. In this framework the free energy is uniquely determined. It proves to be the minimal one in the class of thermodynamically admissible free energies.

How to cite

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Morro, Angelo, and Vianello, Maurizio. "Free energy and internal variables in linear viscoelasticity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 83.1 (1989): 215-219. <http://eudml.org/doc/289253>.

@article{Morro1989,
abstract = {In connection with the determination of the free energy functional for the viscoelastic stress tensor, a viscoelastic material is considered as described by a material with internal variables. In this framework the free energy is uniquely determined. It proves to be the minimal one in the class of thermodynamically admissible free energies.},
author = {Morro, Angelo, Vianello, Maurizio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Free energy; Linear viscoelasticity; Internal variables},
language = {eng},
month = {12},
number = {1},
pages = {215-219},
publisher = {Accademia Nazionale dei Lincei},
title = {Free energy and internal variables in linear viscoelasticity},
url = {http://eudml.org/doc/289253},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Morro, Angelo
AU - Vianello, Maurizio
TI - Free energy and internal variables in linear viscoelasticity
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 215
EP - 219
AB - In connection with the determination of the free energy functional for the viscoelastic stress tensor, a viscoelastic material is considered as described by a material with internal variables. In this framework the free energy is uniquely determined. It proves to be the minimal one in the class of thermodynamically admissible free energies.
LA - eng
KW - Free energy; Linear viscoelasticity; Internal variables
UR - http://eudml.org/doc/289253
ER -

References

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  1. VOLTERRA, V., 1940. Energia nei fenomeni elastici ereditari. Acta Pontificia Acad. Scient., 4: 115-128. Zbl66.1024.02MR25898
  2. GRAFFI, D., 1974. Sull'espressione dell'energia libera nei materiali viscoelastici lineari. Ann. Mat. Pura Appl., 98: 273-279. Zbl0281.73027MR345497DOI10.1007/BF02414027
  3. COLEMAN, B.D., 1964. Thermodynamics of materials with memory. Arch. Rational Mech. Anal., 17: 1-46. MR171419DOI10.1007/BF00283864
  4. MORRO, A., 1990. Topics in the Theory of Materials with Memory. Mediterranean Press, Rende (Italy). 
  5. DAY, W.A., 1972. The Thermodynamics of Simple Materials with Fading Memory. Springer, Berlin. Zbl0295.73007MR366234
  6. MORRO, A. and VIANELLO, M., 1990. Minimal and maximal free energy for materials with memory, Boll. Un. Mat. Ital., 4A: 113-119. Zbl0697.73008MR1047512
  7. GRAFFI, D., 1982. Sull'espressione analitica di alcune grandezze termodinamiche nei materiali con memoria, Rend. Sem. Mat. Univ. Padova, 68: 17-29. Zbl0535.73029
  8. GRAFFI, D., 1986. Ancora sull'espressione analitica dell'energia Ubera nei materiali con memoria. Atti Accad. Sci. Torino, 120: 111-124. 
  9. COLEMAN, B.D. and GURTIN, M. E., 1967. Thermodynamics with internal state variables. J. Chem. Phys., 47: 597-613. 
  10. DAY, W.A., 1976. Entropy and hidden variables in continuum thermodynamics. Arch. Rational Mech. Anal., 62: 367-389. Zbl0387.73004MR431968DOI10.1007/BF00248271
  11. CHEN, P.J. and MORRO, A., 1987. On induced discontinuities in a class of linear materials with internal state parameters. Meccanica, 22: 14-18. Zbl0617.73033

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