A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework

Mechanics Research Communications

Volumn 30, Issue 2, 2003, Pages 109-117

  Rahouadj, Rachid ^a   Ganghoffer, Jean François ^a   Cunat, Christian ^a  

^a NANCY UNIVERSITÉ   (France)

Author keywords

Lagrange formalism; Lie groups of symmetries; Thermodynamics of internal variables (TIV)

Indexed keywords

COMPUTATIONAL METHODS; ENERGY DISSIPATION; ENTROPY; HAMILTONIANS; THERMODYNAMICS;

GIBBS POTENTIAL;

RELAXATION PROCESSES;

EID: 0037368119     PISSN: 00936413     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0093-6413(02)00360-9     Document Type: Article

References (16)

1. Anthony, K.-H., 1986. A new approach to thermodynamics of irreversible processes by means of Lagrange-Formalism. In: Kilmister, C.W. (Ed.), Disequilibrium and Self-Organisation. D. Reidel Publishing Company, pp. 75-82.
2. Burke, W.L., 1997. Applied Differential Geometry. Cambridge University Press.
3. Cunat, C., 1996. Lois Constitutives de Matériaux Complexes Stables ou Vieillissants. Apport de la Thermodynamique de la Relaxation. Rev. Gén. Therm. 35, 680-685.
4. Gyarmati, I., 1970. Non-Equilibrium Thermodynamics. Field Theory and Variational Principles. Springer-Verlag.
5. Lie, S., Engel, F., 1891. Theorie der Transformationsgruppen. Bd 1-2, Leipzig, 632s., 554s., 830s., pp. 1883-1893, Zbl 248.22009.
6. Lie, S., Scheffers, G., 1891. Vorlesungen über Differentialgleichungen mit bekannten infinitesimalen Transformatioonsgruppen. Leipzig, 568s.
7. Marceron, P., 1999. Sur le Rôle des Potentiels Généralisés en Thermodynamique de la Relaxation. Application au Comportement Mécanique des Polymères; Thèse de Doctorat de l'INPL, LEMTA, ENSEM, Nancy.
8. Meixner, J.Z., 1946. Thermodynamische theorie der elastischen relaxation. Z. Naturforsch 4a, 494-600.
9. Mielke, A., 2002. Finite Elastoplasticity, Lie groups and geodesicson SL(d). In: Newton, P., Weinstein, A., Holmes, P. (Eds.), Geometry, Dynamics, and Mechanics. Springer-Verlag.
10. Mrabet, K., Rahouadj, R., Schmitt, J.F., Cunat, C., 2000. A Thermodynamic Modelling of the Viscoplastic behaviour of Semi-Crystalline Polymers. In: 4th Euromech Solids Mechanics Conference (ESMC4). European Mechanics Society, June 26-30, Metz, France.
11. Olver, P.J., 1989. Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, vol. 107, second ed. Springer-Verlag, New York.
12. Ovsiannikov, L.V., 1982. Group Analysis of Differential Equations. Academic Press, New York, translated from Russian by y. Chapovsky.
13. Poincaré, H., 1908. Thermodynamique, deuxième édition, Gauthier-Villars, Paris
14. Prigogine, I., 1955. Introduction to Thermodynamics of Irreversible Processes. Springfield, ed. G. Thomaes.
15. Rahouadj, R., Ganghoffer, J.F., Cunat, C., 2000. Thermodynamics of Relaxation Processes using Internal variables within a Lagrange-formalism. Published in P.Germain's Anniversary Volume 2000. Contiuum Thermomechanics: the Art and Science of Modeling Matter's Behaviour.
16. Tisza, L., 1966. Generalised Thermodynamics. The MIT Press.