Consequences of non-uniqueness in the free energy of materials with memory

International Journal of Engineering Science

Volumn 39, Issue 1, 2001, Pages 53-70

  Golden, J M ^a  

^a DUBLIN INSTITUTE OF TECHNOLOGY   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; FREE ENERGY; ISOTHERMS; RELAXATION PROCESSES; VISCOELASTICITY;

LINEAR ISOTHERMAL RELAXATION FUNCTION;

SHAPE MEMORY EFFECT;

EID: 0035212280     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7225(00)00028-8     Document Type: Article

References (22)

1. Breuer S., Onat E.T. On recoverable work in linear viscoelasticity. Z. Angew. Math. Phys. 15:1964;13-21.
2. Breuer S., Onat E.T. On the determination of free energy in viscoelastic solids. Z. Angew. Math. Phys. 15:1964;185-191.
3. Coleman B.D., Owen D.R. On thermodynamics and elastic-plastic materials. Arch. Rational Mech. Anal. 59:1975;25-51.
4. Day W.A. An objection to using entropy as a primitive concept in continuum thermodynamics. Acta Mech. 27:1977;251-255.
5. Graffi D., Fabrizio M. Non unicità dell'energia libera per i materiali viscoelastici. Atti Acc. Naz. Lincei. 83:1990;209-214.
6. Morro A., Vianello M. Minimal and maximal free energy for materials with memory. Boll. Un. Mat. Ital. 4A:1990;45-55.
7. Fabrizio M., Morro A. Mathematical Problems in Linear Viscoelasticity. 1992;SIAM, Philadelphia.
8. Fabrizio M., Giorgi C., Morro A. Free energies and dissipation properties for systems with memory. Arch. Rational Mech. Anal. 125:1994;341-373.
9. Del Piero G., Deseri L. On the concepts of state and free energy in linear viscoelasticity. Arch. Rational Mech. Anal. 138:1997;1-35.
10. Del Piero G., Deseri L. On the analytic expression of the free energy in linear viscoelasticity. J. Elasticity. 43:1996;247-278.
11. Golden J.M. Free energies in the frequency domain: the scalar case. Quart. Appl. Math. 58:2000;127-150.
12. Deseri L., Gentili G., Golden J.M. An explicit formula for the minimum free energy in linear viscoelasticity. J. Elasticity. 54:1999;141-185.
13. M. Fabrizio, J.M. Golden, Maximum and minimum free energies for a linear viscoelastic material, (1999), submitted for publication.
14. Gurtin M.E., Pipkin A.C. A general theory of heat conduction with finite wave speeds. Arch. Rational Mech. Anal. 31:1968;113-126.
15. McCarthy M.F. Constitutive equations for thermomechanical materials with memory. Int. J. Engrg. Sci. 8:1970;467-474.
16. Coleman B.D. Thermodynamics of materials with memory. Arch. Rational Mech. Anal. 17:1964;1-45.
17. Crochet M.J., Naghdi P.M. A class of simple solids with fading memory. Int. J. Engrg. Sci. 7:1969;1173-1198.
18. Coleman B.D., Noll W. Foundations of linear viscoelasticity. Rev. Mod. Phys. 11:1961;239-249.
19. Morland L.W., Lee E.H. Stress analysis for linear viscoelastic materials with temperature variation. Trans. Soc. Rheol. 4:1960;233-263.
20. Morro A. Wave solutions in linear viscoelastic materials. Graham G.A.C., Walton J.R. Crack and Contact Problems for Viscoelastic Bodies. 1995;Springer, Vienna.
21. Noll W. A new mathematical theory of simple materials. Arch. Rational Mech. Anal. 48:1972;1-50.
22. J.D. Ferry, Viscoelastic Properties of Polymers, third ed., Wiley, New York, 1980.