@article{AIHPA_1978__28_2_155_0, 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://archive.numdam.org/item/AIHPA_1978__28_2_155_0/} }
TY - JOUR AU - Maugin, Gérard A. TI - Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids JO - Annales de l'institut Henri Poincaré. Section A, Physique Théorique PY - 1978 SP - 155 EP - 185 VL - 28 IS - 2 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1978__28_2_155_0/ LA - en ID - AIHPA_1978__28_2_155_0 ER -
%0 Journal Article %A Maugin, Gérard A. %T Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids %J Annales de l'institut Henri Poincaré. Section A, Physique Théorique %D 1978 %P 155-185 %V 28 %N 2 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1978__28_2_155_0/ %G en %F AIHPA_1978__28_2_155_0
Maugin, Gérard A. Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 28 (1978) no. 2, pp. 155-185. http://archive.numdam.org/item/AIHPA_1978__28_2_155_0/
[1] Ondes infinitésimales principales dans les milieux élastiques précontraints en relativité, C. R. Acad. Sci. Paris, 284 A, 1977, p. 393-396. | MR | Zbl
,[2] Infinitésimal Discontinuities in Initially Stressed Relativistic Elastic Solids, Commun. Math. Phys., t. 53, 1977, p. 233-256. | MR | Zbl
,[3] Harmonic Oscillations of Elastic Continua and Detection of Gravitational Waves, J. Gen. Relat. Gravitat., t. 4, 1973, p. 241-272. | MR | Zbl
,[4] 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] 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] Relativistic Theory of the Propagation of Wave Fronts in Nonlinear Elastic Materials, Int. J. Engng. Sci., t. 6, 1968, p. 295-307.
,[7] Speed of Sound in a High-Pressure General Relativistic Solid, Phys. Rev., t. D 7, 1973, p. 1590-1593.
,[8] Magnetized Deformable Media in General Relativity, Ann. Inst. Henri Poincaré, t. A 15, 1971, p. 275-302. | Numdam | MR | Zbl
,[9] Foundations of General Relativistic High-Pressure Elasticity Theory, Proc. Roy. Soc. Lond., t. A 331, 1972, p. 57-83. | MR | Zbl
and ,[10] Mechanics of Continua, J. Wiley, New York, 1967. | Zbl
,[11] Étude des déformations d'un milieu continu..., C. R. Acad. Sci. Paris, t. 273 A, 1971, p. 474-476. | Zbl
,[12] Formulation des lois de comportement en mécanique relativiste des milieux continus, (mimeographed, 164 p.), Univ. Paris VI, 1975.
,[13] 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] Finite Deformation of an Elastic Solid, J. Wiley, New York, 1951. | MR | Zbl
,[15] Equations of State of Continuous Matter in General Relativity, Proc. Roy. Soc. Lond., t. A 316, 1970, p. 1-28.
,[16] 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] 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] Annual Reviews of Astronomy and Astrophysics, vol. 10, Annual Reviews Inc., Palo Alto, Ca., 1972.
, in :[19] General and Exact Theory of Waves in Finite Elastic strains, Arch. Ratl. Mech. Anal., t. 8, 1961, p. 263-296. | MR | Zbl
,[20] Relativistic Theory of Shock Waves, Proc. Roy. Soc. Lond., t. A 259, 1960, p. 129-143. | MR | Zbl
,[21] J. de Physique, t. 30, Suppl. n° 11-12, 1969, p. C3-153-C3-160; Solid STARS, IN Scientific American, Febr. 1971.
,[22] On the Interpretation of Heat in Relativistic Thermodynamics, Phys. Rev., t. 43, 1933, p. 564-568; , Sur le gradient relativiste de température, C. R. Acad. Sci. Paris, t. 278 A, 1974, p. 185-188. | Zbl
and ,[23] Some Problems of the Mechanics of Deformable Media [Translation from the Russian], Noordhoff, Groningen 1962. | MR | Zbl
,[24] Astrophys. J., t. 156, 1969, p. 529.
,[25] Vibrations élastiques excitées par une onde gravitationnelle, Ann. Inst. Henri Poincaré, t. A 16, 1972, p. 63-78. | Numdam | MR | Zbl
,[26] Elastic General Relativistic Systems, J. Math. Phys., t. 13, 1972, p. 1934-1940. | Zbl
and ,[27] A Geometric Generalization of Hooke's Law, J. Math. Phys., t. 14, 1973, p. 1285-1290. | Zbl
and ,[28] Classical Field Theory, J. Wiley, New York, 1976. | MR
,[29] Un problema di equilibrio in relatività generale, Rend. Mat. (6), t. 8, 1975, p. 187-200. | MR | Zbl
and ,[30] 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] 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] On the Covariant Equations of the Relativistic Electrodynamics of Continua-III-Elastic Solids, J. Math. Phys., t. 19, 1978 (in press). | Zbl
,[33] Alger Mathématiques, n° 2, 1958, p. 103 and Géométrie et Relativité, Hermann, Paris, 1964, § 36. | MR
,[34] Ueber die Mechanik des deformierbaren Korpers vom Standpunkte der Relativitätstheorie, Ann. der Phys., t. 36, 1911, p. 493-533. | JFM
,[35] Elastizitätstheorie und Relativitätstheorie, Phys. Zeit., t. 12, 1911, p. 569-575. | JFM
,[36] Zur Elastizitätstheorie vom Standpunkte des Relativitätstheorie, Phys. Zeit., t. 12, 1911, p. 164-169. | JFM
,[37] 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] Allgemeinrelativistische Prinzipien der Kontinuumsmechanik, Ann. Phys. (Leipzig), t. 12, 1964, p. 377-395. | MR | Zbl
,[39] The General Form of Constitutive Equations in Relativistic Physics, Nuovo Cimento, t. 14 B, 1973, p. 57-105. | MR
,[40] Elastic and Thermoelastic Media in General Relativity, Nuovo Cimento, t. 28 B, 1975, p. 377-394. | MR
,[41] On Relativistic Deformable Solids and the Detection of Gravitational Waves, J. Gen. Relat. Gravitat., t. 5, 1974, p. 13-23. | MR | Zbl
,[42] 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] Elasticity and General Relativity, Proc. Roy. Soc. Lond., t. A 272, 1963, p. 44-53. | MR | Zbl
,[44] 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] Sur les Équations de l'élasticité relativiste, C. R. Acad. Sci. Paris, t. 276 A, 1973, p. 1317-1320. | MR | Zbl
and ,[46] Elasticity in General Relativity, Phys. Rev., t. D 1, 1970, p. 1013- 1018. | Zbl
,