no. 2
Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 28 (1978) no. 2, pp. 155-185. 
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     author = {Maugin, G\'erard A.},
     title = {Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {155--185},
     publisher = {Gauthier-Villars},
     volume = {28},
     number = {2},
     year = {1978},
     mrnumber = {495454},
     zbl = {0375.73025},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1978__28_2_155_0/}
}
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Maugin, Gérard A. Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 28 (1978) no. 2, pp. 155-185. http://www.numdam.org/item/AIHPA_1978__28_2_155_0/

[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. | MR | Zbl

[2] G.A. Maugin, Infinitésimal Discontinuities in Initially Stressed Relativistic Elastic Solids, Commun. Math. Phys., t. 53, 1977, p. 233-256. | MR | Zbl

[3] G.A. Maugin, Harmonic Oscillations of Elastic Continua and Detection of Gravitational Waves, J. Gen. Relat. Gravitat., t. 4, 1973, p. 241-272. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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] B. Carter, Speed of Sound in a High-Pressure General Relativistic Solid, Phys. Rev., t. D 7, 1973, p. 1590-1593.

[8] G.A. Maugin, Magnetized Deformable Media in General Relativity, Ann. Inst. Henri Poincaré, t. A 15, 1971, p. 275-302. | Numdam | MR | Zbl

[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. | MR | Zbl

[10] A.C. Eringen, Mechanics of Continua, J. Wiley, New York, 1967. | Zbl

[11] G.A. Maugin, Étude des déformations d'un milieu continu..., C. R. Acad. Sci. Paris, t. 273 A, 1971, p. 474-476. | Zbl

[12] G.A. Maugin, Formulation des lois de comportement en mécanique relativiste des milieux continus, (mimeographed, 164 p.), Univ. Paris VI, 1975.

[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] F.D. Murnaghan, Finite Deformation of an Elastic Solid, J. Wiley, New York, 1951. | MR | Zbl

[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] 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. | Numdam | MR | Zbl

[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. | MR

[18] M. Ruderman, in : Annual Reviews of Astronomy and Astrophysics, vol. 10, Annual Reviews Inc., Palo Alto, Ca., 1972.

[19] C. Truesdell, General and Exact Theory of Waves in Finite Elastic strains, Arch. Ratl. Mech. Anal., t. 8, 1961, p. 263-296. | MR | Zbl

[20] W. Israel, Relativistic Theory of Shock Waves, Proc. Roy. Soc. Lond., t. A 259, 1960, p. 129-143. | MR | Zbl

[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] 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. | Zbl

[23] I.I. Gol'Denblat, Some Problems of the Mechanics of Deformable Media [Translation from the Russian], Noordhoff, Groningen 1962. | MR | Zbl

[24] F.J. Dyson, Astrophys. J., t. 156, 1969, p. 529.

[25] A. Papapetrou, Vibrations élastiques excitées par une onde gravitationnelle, Ann. Inst. Henri Poincaré, t. A 16, 1972, p. 63-78. | Numdam | MR | Zbl

[26] E.N. Glass and J. Winicour, Elastic General Relativistic Systems, J. Math. Phys., t. 13, 1972, p. 1934-1940. | Zbl

[27] E.N. Glass and J. Winicour, A Geometric Generalization of Hooke's Law, J. Math. Phys., t. 14, 1973, p. 1285-1290. | Zbl

[28] D.E. Soper, Classical Field Theory, J. Wiley, New York, 1976. | MR

[29] C. Cattaneo and A. Gerardi, Un problema di equilibrio in relatività generale, Rend. Mat. (6), t. 8, 1975, p. 187-200. | MR | Zbl

[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. | Zbl

[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. | MR

[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). | Zbl

[33] J.-M. Souriau, Alger Mathématiques, n° 2, 1958, p. 103 and Géométrie et Relativité, Hermann, Paris, 1964, § 36. | MR

[34] G. Herglotz, Ueber die Mechanik des deformierbaren Korpers vom Standpunkte der Relativitätstheorie, Ann. der Phys., t. 36, 1911, p. 493-533. | JFM

[35] M. Born, Elastizitätstheorie und Relativitätstheorie, Phys. Zeit., t. 12, 1911, p. 569-575. | JFM

[36] W.V. Ignatowsky, Zur Elastizitätstheorie vom Standpunkte des Relativitätstheorie, Phys. Zeit., t. 12, 1911, p. 164-169. | JFM

[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. | Numdam | MR | Zbl

[38] H.G. Schöpf, Allgemeinrelativistische Prinzipien der Kontinuumsmechanik, Ann. Phys. (Leipzig), t. 12, 1964, p. 377-395. | MR | Zbl

[39] G. Lianis, The General Form of Constitutive Equations in Relativistic Physics, Nuovo Cimento, t. 14 B, 1973, p. 57-105. | MR

[40] C. Barrabes, Elastic and Thermoelastic Media in General Relativity, Nuovo Cimento, t. 28 B, 1975, p. 377-394. | MR

[41] G.A. Maugin, On Relativistic Deformable Solids and the Detection of Gravitational Waves, J. Gen. Relat. Gravitat., t. 5, 1974, p. 13-23. | MR | Zbl

[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. | Numdam | MR | Zbl

[43] C.B. Rayner, Elasticity and General Relativity, Proc. Roy. Soc. Lond., t. A 272, 1963, p. 44-53. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[46] W.C. Hernandez, Elasticity in General Relativity, Phys. Rev., t. D 1, 1970, p. 1013- 1018. | Zbl