×

Exact relativistic theory of wave propagation in prestressed nonlinear elastic solids. (English) Zbl 0375.73025


MSC:

74J99 Waves in solid mechanics
74F05 Thermal effects in solid mechanics
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
PDF BibTeX XML Cite
Full Text: Numdam EuDML

References:

[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 434302 | Zbl 0353.73030 · Zbl 0353.73030
[2] G.A. Maugin , Infinitésimal Discontinuities in Initially Stressed Relativistic Elastic Solids , Commun. Math. Phys. , t. 53 , 1977 , p. 233 - 256 . Article | MR 446005 | Zbl 0354.73031 · Zbl 0354.73031
[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 406314 | Zbl 0365.73002 · Zbl 0365.73002
[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 434303 | Zbl 0355.73028 · Zbl 0355.73028
[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 171441 | Zbl 0131.43102 · Zbl 0131.43102
[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 290744 | Zbl 0234.73037 · Zbl 0234.73037
[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 311270 | Zbl 0249.73093 · Zbl 0249.73093
[10] A.C. Eringen , Mechanics of Continua , J. Wiley , New York , 1967 . Zbl 0222.73001 · Zbl 0222.73001
[11] G.A. Maugin , Étude des déformations d’un milieu continu... , C. R. Acad. Sci. Paris , t. 273 A, 1971 , p. 474 - 476 . Zbl 0218.53043 · Zbl 0218.53043
[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 45548 | Zbl 0045.26504 · Zbl 0045.26504
[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 413994 | Zbl 0321.53021 · Zbl 0321.53021
[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 297295
[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 138259 | Zbl 0111.37703 · Zbl 0111.37703
[20] W. Israel , Relativistic Theory of Shock Waves , Proc. Roy. Soc. Lond. , t. A 259 , 1960 , p. 129 - 143 . MR 127126 | Zbl 0094.41902 · Zbl 0094.41902
[21] M. Ruderman , J. de Physique , t. 30 , Suppl. n^\circ 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 0006.37602 · Zbl 0006.37602
[23] I.I. Gol’Denblat , Some Problems of the Mechanics of Deformable Media [Translation from the Russian], Noordhoff , Groningen 1962 . MR 168168 | Zbl 0111.20101 · Zbl 0111.20101
[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 292472 | Zbl 0236.73044 · Zbl 0236.73044
[26] E.N. Glass and J. Winicour , Elastic General Relativistic Systems , J. Math. Phys. , t. 13 , 1972 , p. 1934 - 1940 . Zbl 0251.73004 · Zbl 0251.73004
[27] E.N. Glass and J. Winicour , A Geometric Generalization of Hooke’s Law , J. Math. Phys. , t. 14 , 1973 , p. 1285 - 1290 . Zbl 0265.73001 · Zbl 0265.73001
[28] D.E. Soper , Classical Field Theory , J. Wiley , New York , 1976 . MR 459481
[29] C. Cattaneo and A. Gerardi , Un problema di equilibrio in relatività generale , Rend. Mat. ( 6 ), t. 8 , 1975 , p. 187 - 200 . MR 401036 | Zbl 0325.73003 · Zbl 0325.73003
[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 0233.73011 · Zbl 0233.73011
[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 164727
[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 0395.76094 · Zbl 0395.76094
[33] J.-M. Souriau , Alger Mathématiques , n^\circ 2 , 1958 , p. 103 and Géométrie et Relativité , Hermann , Paris , 1964 , 36 . MR 172679 · Zbl 0117.22204
[34] G. Herglotz , Ueber die Mechanik des deformierbaren Korpers vom Standpunkte der Relativitätstheorie , Ann. der Phys. , t. 36 , 1911 , p. 493 - 533 . JFM 42.0863.02 · JFM 42.0863.02
[35] M. Born , Elastizitätstheorie und Relativitätstheorie , Phys. Zeit. , t. 12 , 1911 , p. 569 - 575 . JFM 42.0726.01 · JFM 42.0726.01
[36] W.V. Ignatowsky , Zur Elastizitätstheorie vom Standpunkte des Relativitätstheorie , Phys. Zeit. , t. 12 , 1911 , p. 164 - 169 . JFM 42.0865.01 · JFM 42.0865.01
[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 189753 | Zbl 0131.43002 · Zbl 0131.43002
[38] H.G. Schöpf , Allgemeinrelativistische Prinzipien der Kontinuumsmechanik , Ann. Phys. ( Leipzig ), t. 12 , 1964 , p. 377 - 395 . MR 167307 | Zbl 0116.21602 · Zbl 0116.21602
[39] G. Lianis , The General Form of Constitutive Equations in Relativistic Physics , Nuovo Cimento , t. 14 B, 1973 , p. 57 - 105 . MR 373540
[40] C. Barrabes , Elastic and Thermoelastic Media in General Relativity , Nuovo Cimento , t. 28 B, 1975 , p. 377 - 394 . MR 389118
[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 406315 | Zbl 0356.73025 · Zbl 0356.73025
[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 391877 | Zbl 0328.73026 · Zbl 0328.73026
[43] C.B. Rayner , Elasticity and General Relativity , Proc. Roy. Soc. Lond. , t. A 272 , 1963 , p. 44 - 53 . MR 149930 | Zbl 0108.21603 · Zbl 0108.21603
[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 173521 | Zbl 0125.20903 · Zbl 0125.20903
[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 317624 | Zbl 0286.73019 · Zbl 0286.73019
[46] W.C. Hernandez , Elasticity in General Relativity , Phys. Rev. , t. D 1 , 1970 , p. 1013 - 1018 . Zbl 0212.57202 · Zbl 0212.57202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.