Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids

Gérard A. Maugin

Annales de l'I.H.P. Physique théorique (1978)

  • Volume: 28, Issue: 2, page 155-185
  • ISSN: 0246-0211

How to cite

top

Maugin, Gérard A.. "Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids." Annales de l'I.H.P. Physique théorique 28.2 (1978): 155-185. <http://eudml.org/doc/75976>.

@article{Maugin1978,
author = {Maugin, Gérard A.},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {2},
pages = {155-185},
publisher = {Gauthier-Villars},
title = {Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids},
url = {http://eudml.org/doc/75976},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Maugin, Gérard A.
TI - Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids
JO - Annales de l'I.H.P. Physique théorique
PY - 1978
PB - Gauthier-Villars
VL - 28
IS - 2
SP - 155
EP - 185
LA - eng
UR - http://eudml.org/doc/75976
ER -

References

top
  1. [1] G.A. Maugin, Ondes infinitésimales principales dans les milieux élastiques précontraints en relativité, C. R. Acad. Sci. Paris, 284 A, 1977, p. 393-396. Zbl0353.73030MR434302
  2. [2] G.A. Maugin, Infinitésimal Discontinuities in Initially Stressed Relativistic Elastic Solids, Commun. Math. Phys., t. 53, 1977, p. 233-256. Zbl0354.73031MR446005
  3. [3] G.A. Maugin, Harmonic Oscillations of Elastic Continua and Detection of Gravitational Waves, J. Gen. Relat. Gravitat., t. 4, 1973, p. 241-272. Zbl0365.73002MR406314
  4. [4] G.A. Maugin, Théorie relativiste exacte de la propagation des fronts d'onde principaux dans les milieux élastiques nonlinéaires isotropes et précontraints, C. R. Acad. Sci. Paris, t. 284 A, 1977, p. 719-722. Zbl0355.73028MR434303
  5. [5] A. Bressan, Onde ordinarie di discontinuita nei mezzi elastici con deformazioni finite in relatività generale, Riv. Mat. Univ. Parma (2), t. 4, 1963, p. 23-40. Zbl0131.43102MR171441
  6. [6] R.A. Grot, Relativistic Theory of the Propagation of Wave Fronts in Nonlinear Elastic Materials, Int. J. Engng. Sci., t. 6, 1968, p. 295-307. 
  7. [7] B. Carter, Speed of Sound in a High-Pressure General Relativistic Solid, Phys. Rev., t. D 7, 1973, p. 1590-1593. 
  8. [8] G.A. Maugin, Magnetized Deformable Media in General Relativity, Ann. Inst. Henri Poincaré, t. A 15, 1971, p. 275-302. Zbl0234.73037MR290744
  9. [9] B. Carter and H. Quintana, Foundations of General Relativistic High-Pressure Elasticity Theory, Proc. Roy. Soc. Lond., t. A 331, 1972, p. 57-83. Zbl0249.73093MR311270
  10. [10] A.C. Eringen, Mechanics of Continua, J. Wiley, New York, 1967. Zbl0222.73001
  11. [11] G.A. Maugin, Étude des déformations d'un milieu continu..., C. R. Acad. Sci. Paris, t. 273 A, 1971, p. 474-476. Zbl0218.53043
  12. [12] G.A. Maugin, Formulation des lois de comportement en mécanique relativiste des milieux continus, (mimeographed, 164 p.), Univ. Paris VI, 1975. 
  13. [13] G.A. Maugin, The Principle of Material Frame Indifference in General Relativity... in : Ondes et Radiations Gravitationnelles, (proc. Coll. Intern. C. N. R. S., Paris, 1973), p. 331-338, Ed. C. N. R. S., Paris, 1974. 
  14. [14] F.D. Murnaghan, Finite Deformation of an Elastic Solid, J. Wiley, New York, 1951. Zbl0045.26504MR45548
  15. [15] J.G. Olroyd, Equations of State of Continuous Matter in General Relativity, Proc. Roy. Soc. Lond., t. A 316, 1970, p. 1-28. 
  16. [16] G.A. Maugin, Conditions de compatibilité pour une hypersurface singulière en mécanique relativiste des milieux continus, Ann. Inst. Henri Poincaré, t. A 24, 1976, p. 213-241. Zbl0321.53021MR413994
  17. [17] A. Lichnerowicz, Ondes de choc, ondes infinitésimales..., in: Relativistic Fluid Dynamics (C. I. M. E., Bressanone, 1970), Ed. C. Cattaneo, p. 87-204, Cremonese, Rome, 1971. MR297295
  18. [18] M. Ruderman, in : Annual Reviews of Astronomy and Astrophysics, vol. 10, Annual Reviews Inc., Palo Alto, Ca., 1972. 
  19. [19] C. Truesdell, General and Exact Theory of Waves in Finite Elastic strains, Arch. Ratl. Mech. Anal., t. 8, 1961, p. 263-296. Zbl0111.37703MR138259
  20. [20] W. Israel, Relativistic Theory of Shock Waves, Proc. Roy. Soc. Lond., t. A 259, 1960, p. 129-143. Zbl0094.41902MR127126
  21. [21] M. Ruderman, J. de Physique, t. 30, Suppl. n° 11-12, 1969, p. C3-153-C3-160; Solid STARS, IN Scientific American, Febr. 1971. 
  22. [22] R.C. Tolman and H.P. Robertson, On the Interpretation of Heat in Relativistic Thermodynamics, Phys. Rev., t. 43, 1933, p. 564-568; G.A. Maugin, Sur le gradient relativiste de température, C. R. Acad. Sci. Paris, t. 278 A, 1974, p. 185-188. Zbl0006.37602
  23. [23] I.I. Gol'Denblat, Some Problems of the Mechanics of Deformable Media [Translation from the Russian], Noordhoff, Groningen1962. Zbl0111.20101MR168168
  24. [24] F.J. Dyson, Astrophys. J., t. 156, 1969, p. 529. 
  25. [25] A. Papapetrou, Vibrations élastiques excitées par une onde gravitationnelle, Ann. Inst. Henri Poincaré, t. A 16, 1972, p. 63-78. Zbl0236.73044MR292472
  26. [26] E.N. Glass and J. Winicour, Elastic General Relativistic Systems, J. Math. Phys., t. 13, 1972, p. 1934-1940. Zbl0251.73004
  27. [27] E.N. Glass and J. Winicour, A Geometric Generalization of Hooke's Law, J. Math. Phys., t. 14, 1973, p. 1285-1290. Zbl0265.73001
  28. [28] D.E. Soper, Classical Field Theory, J. Wiley, New York, 1976. MR459481
  29. [29] C. Cattaneo and A. Gerardi, Un problema di equilibrio in relatività generale, Rend. Mat. (6), t. 8, 1975, p. 187-200. Zbl0325.73003MR401036
  30. [30] C. Cattaneo, Essai d'une théorie relativiste de l'élasticité, C. R. Acad. Sci. Paris, t. 272 A, 1971, p. 1421-1424 ; Équations relativistes des petits mouvements adiabatiques d'un corps élastique, ibid., t. 273 A, 1971, p. 533-536 ; Élasticité relativiste, Symposia Mathematica, vol. XII, p. 337-352, Ist. di Alta Matematica, Academic Press, New York, 1973. Zbl0233.73011
  31. [31] A.H. Taub, Small Motions of Spherically Symmetric Distributions of Matter, in: Les Théories relativistes de la gravitation (Coll. Royaumont, 1959), p. 173-191, Ed. C. N. R. S., Paris, 1962. MR164727
  32. [32] G.A. Maugin, On the Covariant Equations of the Relativistic Electrodynamics of Continua-III-Elastic Solids, J. Math. Phys., t. 19, 1978 (in press). Zbl0395.76094
  33. [33] J.-M. Souriau, Alger Mathématiques, n° 2, 1958, p. 103 and Géométrie et Relativité, Hermann, Paris, 1964, § 36. MR172679
  34. [34] G. Herglotz, Ueber die Mechanik des deformierbaren Korpers vom Standpunkte der Relativitätstheorie, Ann. der Phys., t. 36, 1911, p. 493-533. Zbl42.0863.02JFM42.0863.02
  35. [35] M. Born, Elastizitätstheorie und Relativitätstheorie, Phys. Zeit., t. 12, 1911, p. 569-575. Zbl42.0726.01JFM42.0726.01
  36. [36] W.V. Ignatowsky, Zur Elastizitätstheorie vom Standpunkte des Relativitätstheorie, Phys. Zeit., t. 12, 1911, p. 164-169. Zbl42.0865.01JFM42.0865.01
  37. [37] A. Bressan, Termodinamica e magneto-visco-elasticita con deformazioni finite in relatività generale, Rend. Sem. Mat. Univ. Padova, t. 34, 1964, p. 1-73. Zbl0131.43002MR189753
  38. [38] H.G. Schöpf, Allgemeinrelativistische Prinzipien der Kontinuumsmechanik, Ann. Phys. (Leipzig), t. 12, 1964, p. 377-395. Zbl0116.21602MR167307
  39. [39] G. Lianis, The General Form of Constitutive Equations in Relativistic Physics, Nuovo Cimento, t. 14 B, 1973, p. 57-105. MR373540
  40. [40] C. Barrabes, Elastic and Thermoelastic Media in General Relativity, Nuovo Cimento, t. 28 B, 1975, p. 377-394. MR389118
  41. [41] G.A. Maugin, On Relativistic Deformable Solids and the Detection of Gravitational Waves, J. Gen. Relat. Gravitat., t. 5, 1974, p. 13-23. Zbl0356.73025MR406315
  42. [42] R. Gambini, Vibrations excitées par une onde gravitationnelle dans les milieux élastiques et viscoélastiques, Ann. Inst. Henri Poincaré, t. A 23, 1975, p. 389-406. Zbl0328.73026MR391877
  43. [43] C.B. Rayner, Elasticity and General Relativity, Proc. Roy. Soc. Lond., t. A 272, 1963, p. 44-53. Zbl0108.21603MR149930
  44. [44] J.F. Bennoun, Sur les représentations hydrodynamique et thermodynamique des milieux élastiques en relativité générale, C. R. Acad. Sci. Paris, t. 259 A, 1964, p. 3705-3708. Zbl0125.20903MR173521
  45. [45] Y. Choquet-Bruhat and L. Lamoureux-Brousse, Sur les Équations de l'élasticité relativiste, C. R. Acad. Sci. Paris, t. 276 A, 1973, p. 1317-1320. Zbl0286.73019MR317624
  46. [46] W.C. Hernandez, Elasticity in General Relativity, Phys. Rev., t. D 1, 1970, p. 1013- 1018. Zbl0212.57202

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.