General references. - Springer978-3-642-46… · · 2017-08-24General references. ... On the...

542 C. TRUESDELL and W. NOLL: Non-Linear Field Theories of Mechanics.

General references.

Of the books and reviews which lay any claim to covering a large part of the subject treated here, none can be recommended as trustworthy. Reference to works developing further matters of detail has been made at appropriate points in the treatise.

List of Works Cited. This list, not attempting to be a complete bibliography of the subject, is limited to works

consulted by the authors in writing the treatise. Italic numbers in parentheses following the reference indicate the sections in which it has been cited.

1678 [1] HOOKE, R.: Lectures de Potentia Restitutiva, or of Spring Explaining the Power of Springing Bodies. London = R. T. GUNTHER: Early Science in Oxford 8, 331-356 (1931). (19A)

1769 [1] EULER, L.: De aequilibrio et motu corporum flexuris elasticis iunctorum. N ovi comm. acado sci. Petrop. 13 (1768), 259-304 = Opera omnia II 11, 3-16. (66)

1780 [1] COULOMB, C. A.: Recherches sur la meilleure maniere de fabriquer les aiguilles aimantees ... Mem. math. phys. divers sayans 9, 165-264. (66)

1787 [1] COULOMB, C. A.: Recherches tMoriques et experimentales sur la force de torsion, et sur l'elasticite de fils de metal: Application de cette tMorie a l'emploi des metaux dans les arts et dans differentes experiences de physique: Construction de differentes balances de torsion, pour mesurer les plus petits degres de force. Observations sur les loix de l'elasticite et de la coherence. Mem. acado sci. Paris

1807 [1]

1823 [1]

1828 [1]

1829 [1]

1831 [1]

1836 [1]

1839 [1J

1841 [1J

1843 [1]

1844 [1]

1845 [1]

1847 [1]

1849 [1]

1850 [1]

[2]

1784,229-272. (66) YOUNG, T.: Mathematical Elements of Natural Philosophy. A Course of Lectures on Natural Philosophy and the Mechanical Arts 2, 1-86. London. (66) CAUCHY, A.-L.: Recherches sur l'equilibre et Ie mouvement interieur des corps solides ou fluides, elastiques ou non elastiques. Bull. Soc. Philomath. Paris 9-13 = Oeuvres (2) 2, 300-304. (43) CAUCHY, A.-L.: Sur les equations qui expriment les conditions d'equilibre ou les lois du mouvement interieur d'un corps solide, elastique ou non elastique. Ex. de Math. 3, 160-187 = Oeuvres (2) 8, 253-277. (26,43) CAUCHY, A.-L.: Sur l'equilibre et Ie mouvement interieur des corps consideres comme des masses continues. Ex. de Math. 4, 293-319 = Oeuvres 9,243-369. (19A, 68, 99) POISSON, S.-D.: Memoire sur les equations generales de l'equilibre et du mouvement des corps elastiques et des fluides (1829). J. Ecole Poly. 13, Cahier 20, 1-174. (19A) PIOLA, G.: Nuova analisi per tutte Ie questioni della meccanica molecolare. Mem. Mat. Fis. Soc. Ital. Modena 21 (1835), 155-231. (94) GREEN, G.: On the laws of reflection and refraction of light at the common surface of two non-crystallised media (1837). Trans. Cambridge Phil. Soc. 7 (1838-1842) 1-24 = Papers, 245-269. (82A, 88) GREEN, G.: On the propagation of light in crystallised media (1839). Trans. Cambridge Phil. Soc. 7 (1838-1842), 121-140 = Papers, 293-311. (82A, 84) ST. VENANT, A.-J.-C. B. DE: Note a joindre au memoire sur la dynamique des fluides, presente Ie 14 avril 1834. C. R. Acad. Sci. Paris 17, 1240-1243. (54,119) ST. VENANT, A.-J.-C. B. DE: Sur les pressions qui se developpent a l'interieur des corps solides lorsque les deplacements de leurs points, sans alterer l'elasticite, ne peuvent cependant pas etre consideres comme tres petits. Bull. Soc. Philomath. 5, 26-28. (94) STOKES, G. G.: On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Cambridge Phil. Soc. 8 (1844-1849),287-319 = Papers 1,75-129. (26,119) Sr. VENANT, A.-J.-C. B. DE: Memoire sur l'equilibre des corps solides, dans les limites de leur elasticite, et sur les conditions de leur resistance, quand les deplacements eprouves par leurs points ne sont pas tres-petits. C. R. Acad. Sci. Paris 24, 260-263. (94) HAUGHTON, S.: On the equilibrium and motion of solid and fluid bodies (1846). Trans. Roy. Irish Acad. 21, 151-198. (88) CAUCHY, A.-L.: Memoire sur les systemes isotropes de points materiels. Mem. Acad. Sci. Paris 22,615-654 = Oeuvres (1) 2, 351-386. (11) KIRCHHOFF, G.: "Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe. J. reine angew. Math. 40, 51-88 = Ges. Abh. 237-279. (82A, 88)

List of Works Cited. 543

1851 [lJ CAUCHY, A.-L.: Note sur l'equilibre et les mouvements vibratoires des corps solides. C. R. Acad. Sci. Paris 32, 323-326 = Oeuvres (1) 11, 341-346. (28,98)

[2J DA SILVA, D. A.: Memoria sobre a rotac;:ao das forc;:as em torno dos pontos d'applicac;:ao. Mem. Ac. Sc. Lisboa (2a) 31 , 61-231. (44)

1852 [1] KIRCHHOFF, G.: Uber die Gleichungen des Gleichgewichts eines elastischen Korpers bei nicht unendlich kleinen Verschiebungen seiner Theile. Sitzgsber. Akad. Wiss. Wien 9, 762-773. (Not repro in Abh.) (82, 82A, 94)

1853 [I] MAXWELL, J. C.: On the equilibrium of elastic solids (1850). Trans. Roy. Soc. Edinb. 20 (1848/1853), 87-120 = Papers I, 30--73. (66)

1855 [1] ST. VENANT, A.-J.-C. B. DE: Memoire sur la torsion des prismes ... (1853). Mem. Divers Savants Acad. Sci. Paris 14, 233-560. (66)

[2] THOMSON, W. (Lord KELVIN): On the thermo-elastic and thermo-magnetic properties of matter. Quart. J. Math. 1 (1855-1857), 55-77 = (with notes and additions) Phil. Mag. (5) 5 (1878), 4-27 = Pt. VII of On the dynamical theory of heat. Papers I, 291-316. (82A, 83)

1856 [1] THOMSON, W. (Lord KELVIN): Elements of a mathematical theory of elasticity. Phil. Trans. Roy. Soc. Lond. 146,481-498. (82A)

1860 [1] NEUMANN, C.: Zur Theorie der Elasticitat. J. reine angew. Math. 57, 281-318. (82,82A)

1863 [1] ST. VENANT, A.-J.-C. B. DE: Memoire sur la distribution des elasticites autour de chaque point d'un solide ou d'un milieu de contexture quelconque, particulierement lorsqu'il est amorphe sans etre isotrope. J. Math. Pures Appl. (2) 8,257-295, 353-430. (84, 94)

[2J THOMSON, W. (Lord KELVIN): Dynamical problems regarding elastic spheroidal shells and spheroids of incompressible liquid. Phil. Trans. Roy. Soc. Lond. A 153, 583-616 = Papers 3, 351-394. (82A, 83, 84, 85)

1866 [1] KLEITZ, C.: Sur les forces moleculaires dans les liquides en mouvement avec application a l'hydrodynamique. C. R. Acad. Sci. Paris 63, 988-991. (Partial abstract of [1873,1]). (119)

1867 [1] MAXWELL, J. C.: On the dynamical of theory gases (1866). Phil. Trans. Roy. Soc. Lond. A 157, 49-88 = Phil. Mag. (4) 35 (1868),129-145,185-217 = Papers 2, 26-78. (35)

[2J THOMSON, W. (Lord KELVIN), and P. G. TAIT: Treatise on Natural Philosophy, Part 1. Cambridge. [The second edition, which appeared in 1879, has been reprinted by Dover Publications, N.Y., under the redundant as well as gratuitous title, "Principles of Mechanics and Dynamics".] (54,82A)

1868 [1] BOUSSINESQ, J.: Sur l'influence des frottements dans les mouvements reguliers des fluides. J. Math. Pures Appl. (2) 13, 377-438. (119,120,125)

[2] ST. VENANT, A.-J.-C. B. DE: Formules de l'elasticite des corps amorphes que des compressions permanentes et inegales ont rendus heterotropes. J. Math. Pures Appl. (2) 13, 242-254. (68)

1869 [1] ST. VENANT, A.- J.-C. B. DE: Note sur les valeurs que prennent les pressions dans un solide elastique isotrope lorsque l'on tient compte des derivees d'ordre superieur des deplacements tres-petits que leurs points ont eprouves. C. R. Acad. Sci. Paris 68, 569-571. (28, 98)

[2] ST. VENANT, A.- J.-C. B. DE: Rapport sur un memoire de M. MAURICE LEVY, relatif a l'hydrodynamique des liquides homogenes, particulierement a leur ecoulement rectiligne et permanent. C. R. Acad. Sci. Paris 68, 582-592. (28, 119)

1870 [I] BOUSSINESQ, J.: Note complementaire au memoire sur les ondes liquides periodiques, presente Ie 29 novembre 1869, et approuve par l'Academie Ie 21 fevrier 1870. - Etablissement de relations generales et nouvelles entre l'energie interne d'un corps fluide ou solide, et ses pressions ou forces elastiques. C. R. Acad. Sci. Paris 71, 400-402. (84, 94)

1871 [1] ST. VENANT, A.- J.-C. B. DE: Formules des augmentations que de petites deformations d'un solide apportent aux pressions ou forces elastiques, supposees considerables, qui deja etaient en jeu dans son interieur. J. Math. Pures Appl. (2) 16,275-307. (94)

1872 [1] BOUSSINESQ, J.: Tbeorie des ondes liquides periodiques (1869). Mem. Divers Savants 20, 509-615. Abstracts in C. R. Acad. Sci. Paris 68, 905-906 (1869); 70, 360-367 (1870), supplemented by [1870,1]. (82,84)

[2] Sr. VENANT, A.- J.-C. B. DE: Rapport sur un memoire de M. KLEITZ intitule: Etudes sur les forces moleculaires dans les liquides en mouvement, et application a l'hydrodynamique. C. R. Acad. Sci. Paris 74, 426-438. (119)

[3] ST. VENANT, A.- J.-C. B. DE: Sur l'hydrodynamique des cours d'eau. C. R. Acad. Sci. Paris 74, 570--577. 649-657, 693-701, 770--774. (119)

544

1873 [1]

1874 [1]

[2]

[3]

1875 [1]

[2]

1876 [1]

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1883 [1]

1885 [1]

1886 [1]

1887 [1]

[2]

1888 [1]

[2]

[3]

1889 [1]

[2]

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1891 [1] 1892 [1]

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1893 [1]

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[5]

C. TRUESDELL and W. NOLL: Non-Linear Field Theories of Mechanics.

KLEITZ, C.: Etudes sur les forces moleculaires dans les liquides en mouvement et application a l'hydrodynamique. Paris: Dunod. (119) BOLTZMANN, L.: Zur Theorie der elastischen Nachwirkung. Sitzgsber. Akad. Wiss. Wien 70 2, 275-306 = Ann. Physik, Erganz. 7, 624-654 (1876) = Wiss. Abh. 1, 616-639. (35,41) MEYER, O.-E.: Zur Theorie der inneren Reibung. J. reine angew. Math. 78, 130-135. (35, 41, 119) MEYER, O.-E.: Theorie der elastischen Nachwirkung. Ann. Physik 151 = (6) 1, 108-119. (35,41,120) GIBBS, J. W.: On the equilibrium of heterogeneous substances. Trans. Conn. Acad. 3 (1875-1878), 108-248, 343-524 = Works 1, 55-353. (82, 82A, 89) MEYER, O. E.: Zusatz zu der Abhandlung zur Theorie der inneren Reibung. J. reine angew. Math. 80, 315-316. (35,41) BUTCHER, J. G.: On viscous fluids in motion. Proc. Lond. Math. Soc. 8 (1876/77), 103-135. (35) MAXWELL, J. c.: On stresses in rarified gases arising from inequalities of temperature. Phil. Trans. Roy Soc. Lond. 170,231-256= Papers 2, 680-712. (124) MACH, E.: Die Mechanik in ihrer Entwicklung, historisch-kritisch dargestellt. Leipzig: Brockhaus. [There are many later editions and translations.] (18) REYNOLDS, 0.: On the dilatancy of media composed of rigid particles in contact. With experimental illustrations. Phil. Mag. (2) 20, 469-481 = Papers 2, 203-216. (119) TODHUNTER, 1., and K. PEARSON: A History of the Theory of Elasticity and of the Strength of Materials from Galilei to Lord Kelvin, 1 [This is mainly the workof PEARSON, as indicated in the enumeration of sections.] Cambridge: Cambridge Univ. Press. Reprinted, Dover Publications, New York, 1960. (50) REYNOLDS, 0.: Experiments showing dilatancy, a property of granular material, possibly connected with gravitation. Proc. Roy. Inst. Gt. Britain 11, 354-363 = Papers 2, 217-227. (119) VOIGT, W.: Theoretische Studien tiber die Elasticitatsverhaltnisse der Krystalle. Abh. Ges. Wiss. Gottingen 34, 100 pp. (98) BARUS, C.: MAXWELL'S theory of the viscosity of solids and its physical verification. Phil. Mag. (5) 26, 183-217. (2) BASSET, A. B.: A Treatise on Hydrodynamics. 2 vols. Cambridge: Cambridge Univ. Press. (120) THOMSON, W. (Lord KELVIN): On the reflection and refraction of light. Phil. Mag. (5) 26,414-425. Reprinted in part as §§ 107-111 of Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. London: Clay & Sons 1904. (51) PEARSON, K.: On the generalized equations of elasticity, and their application to the wave theory of light. Proc. Lond. Math. Soc. 20, 297-350. (35) POINCARE, H.: Le~ons sur la Theorie Mathematique de la Lumiere. Paris. (30, 82A) VOIGT, W.: Uber adiabatische Elasticitatsconstanten. Ann. Physik 36, 743-759. (82A) VOIGT, W.: Uber die innere Reibung der festen Korper, insbesondere der Krystalle. Gottinger Abh. 36, No. 1. (35) SCHOENFLIESS, A.: Kristallsysteme und Kristallstruktur. Leipzig. (33) POINCARE, H.: Le~ons sur la Theorie de l'Elasticite. Paris. (30,68, 82A) VOIGT, W.: Uber innere Reibung fester Korper, insbesondere der Metalle. Ann. Physik (2) 47, 671-693. (35) VOIGT, W.: Bestimmung der Constanten der Elasticitat und Untersuchung der inneren Reibung fUr einige Metalle. Gottinger Abh. 38, No.2. (35) BARUS, C.: Note on the dependence of viscosity on pressure and temperature. Proc. Amer. Acad. Arts Sci. (2) 19 = 27, 13-18. (114) BARUS, C.: Isothermals, isopiestics, and isometrics relative to viscosity. Amer. J. Sci. (3) 45 = 145, 87-96. (114) CELLERIER, G.: Sur les principes generaux de la thermodynamique et leur application aux corps elastiques. Bull. Soc. Math. France 21, 26-43. (43) TODHUNTER, I., and K. PEARSON: A History of the Theory of Elasticity and of the Strength of Materials from Galilei to Lord Kelvin, 2 [almost entirely the work of PEARSON] Cambridge: Cambridge Univ. Press. Reprinted Dover Publications, New York, 1960. (66) VOIGT, W.: Uber eine anscheinend nothwendige Erweiterung der Theorie der Elasticitat. Gottinger Nachr. 534-552 = Ann. Physik (2) 52, 536-555. (66)


1894 [1] FINGER, J.: Das Potential der inneren Krafte und die Beziehungen zwischen den Deformationen und den Spannungen in elastisch isotropen Korpern bei Berucksichtigung von Gliedern, die bezuglich der Deformationselemente von dritter, beziehungsweise zweiter Ordnung sind. Sitzgsber. Akad. Wiss. Wien (Ha) 103, 163-200, 231-250. (66,86)

[2] FINGER, J.: ttber das Kriterion der Coaxialitat zweier Mittelpunktsflachen zweiter Ordnung. Sitzgsber. Akad. Wiss. Wien (Ha) 103, 1061-1065. (48)

[3] FINGER, J.: ttber die allgemeinsten Beziehungen zwischen Deformationen und den zugehorigen Spannungen in aeolotropen und isotropen Substanzen. Sitzgsber. Akad. Wiss. Wien (Ha) 103, 1073-1100. (12, 48, 85, 86)

1895 [1] VOIGT, W.: ttber Medien ohne innere Krafte und eine durch sie gelieferte mechanische Deutung der Maxwell-Hertzschen Gleichungen. Abh. Ges. Wiss. Gottingen 1894, 72-79. (98)

1896 [1] COSSERAT, E., and F.: Sur la tMorie de l'elasticite. Ann. Toulouse 10, 1-116. (4, 42, 43, 83, 84, 85)

1900 [1] BRILLOUIN, M.: TMorie moleculaire des gaz. Diifusion du mouvement et de l'energie. Ann. Chim. (7) 20, 440-485. (125)

1901 [1] DUHEM, P.: Sur les theoremes D'HuGONIOT, les lemmes de M. HADAMARD et la propagation des ondes dans les fluides visqueux. C. R. Acad. Sci. Paris 132, 117-120. (96t)

[2] DUIIEM, P.: Des ondes qui peuvent persister en un fluide visqueux. C. R. Acad. Sci. Paris 133, 579--580. (96t)

[3] HADAMARD, J.: Sur la propagation des ondes. Bull. Soc. Math. France 29, 50-60. (71, 74,90)

[4] KORTEWEG, D. J.: Sur la forme que prennent les equations du mouvement des fluides si l'on tient compte des forces capillaires causees par des variations de densite considerables mais continues et sur la tMorie de la capillarite dans l'hypothese d'une variation continue de la densite. Arch. Neerl. Sci. Ex. Nat. (2) 6, 1-24. (124)

[5] NATANSON, L.: On the laws of viscosity. Phil. Mag. (6) 2, 342-356. (19A, 35) [6] NATANSON, L.: Sur les lois de la viscosite. Bull. Int. Acad. Sci. Cracovie 95-111.

(19A,35) [7] NATANSON, L.: Sur la double refraction accidentelle dans les liquides. Bull. Int.

Acad. Sci. Cracovie 161-1 71. (19 A, 35) [8] NATANSON, L.: ttber die Gesetze der inneren Reibung. Z. physik. Chem. 38,

690-704. (19A, 35) [9] REYNOLDS, 0.: On the equations of motion and the boundary conditions for

viscous fluids (1883). Papers 2, 132-137. (35) 1902 [1] DUHEM, P.: Recherches sur l'hydrodynamique. Seconde Partie. Ann. Toulouse

(2) 4, 101-169. Also included in reprint, Paris: Gauthier Villars 1903. (96t) [2] NATANSON, L.: Sur la propagation d'un petit mouvement dans un fluide visqueux.

Bull. Int. Acad. Sci. Cracovie 19-35. (19A) [3] NATANSON, L.: Sur la fonction dissipative d'un fluide visqueux. Bull. Int. Acad.

Sci. Cracovie 448-494. (19A) [4] NATANSON, L.: Sur la deformation d'un disque plastico-visqueux. Bull. Int. Acad.

Sci. Cracovie 494-512. (19A) [5] NATANSON, L.: Sur la conductibilite calorifique d'un gaz en mouvement. Bull.

Int. Acad. Sci. Cracovie 137-146. (19A) 1903 [1] DUHEM, P.: Sur la viscosite en un milieu vitreux. C. R. Acad. Sci. Paris 136,

281-283. (41) [2] DUHEM, P.: Sur les equations du mouvement et la relation supplementaire au

sein d'un milieu vitreux. C. R. Acad. Sci. Paris 136, 343-345. (41, 71) [3] DUHEM, P.: Sur la propagation des ondes dans un milieu parfaitement elastique

affect6 de deformations finies. C. R. Acad. Sci. Paris 136, 1379-1381. (90) [4] HADAMARD, J.: Le~ons sur la Propagation des Ondes et les Equations de I'Hydro

dynamique. Paris: Hermann. (31, 68b, 71, 74, 88, 89, 90) [5] N ATANSON, L. : ttber einige von Herrn B. WEINSTEIN zu Meiner Theorie der inneren

Reibung gemachten Bemerkungen. Physik. Z. 4, 541-543. (19A) [6] NATANSON, L.: Sur l'application des equations de Lagrange dans la tMorie de la

viscosite. Bull. Int. Acad. Sci. Cracovie 268-283. (19A) [7] NATANSON, L.: Sur l'approximation de certaines equations de la tMorie de la

viscosite. Bull. Int. Acad. Sci. Cracovie 283-311. (19A) [8] ZAREMBA, S.: Remarques sur les travaux de M. NATANSON relatifs a la tMorie

de la viscosite. Bull. Int. Acad. Sci. Cracovie 85-93. (19A, 35) Handbuch der Physik, Bd. 111/3. 35


[9J ZAREMBA, S.: Sur une generalisation de la theorie classique de la viscosite. Bull. Int. Acad. Sci. Cracovie 380-403. (19A, 35)

[10] ZAREMBA, S.: Sur un probleme d'hydrodynamique lie a un cas double refraction accidentale dans les liquides et sur les considerations theoriques de M. NATANSON relatives a ce phenomene. Bull. Int. Acad. Sci. Cracovie 403-423. (19A, 35)

[11] ZAREMBA, S.: Sur une forme perfectionnee de la theorie de la relaxation. Bull. Int. Acad. Sci. Cracovie 594-614. (19A, 35,36,99,119)

[12] ZAREMBA, S.: Le principe des mouvements relatifs et les equations de la mecanique physique. Bull. Int. Acad. Sci. Cracovie 614-621. (19A, 35, 36, 99, 119)

1904 [1] DUHEM, P.: Recherches sur l'elasticite, Premiere Partie. De l'equilibre et du mouvement des milieux vitreux. Ann. Ecole Normale (3) 21, 99-141. Repr. Paris: Gauthier-Villars 1906. (41)

1905 [1] DUHEM, P.: Recherches sur l'elasticite, Troisieme Partie. La stabilite des milieux elastiques. Ann. Ecole Norm. (3) 22, 143-217. Repr. Paris: Gauthier-Villars 1906. (52, 68b, 88,89)

[2] POINCARE, H.: Science and Hypothesis. Trans!. W. J. G. London. (3) [3J POYNTING, J. H.: Radiation-pressure. Phil. Mag. 9, 393-406 = Papers 2,

335-346. (54, 66) 1906 [1] DUHEM, P.: Recherches sur l'elasticite. Quatrieme Partie. Proprietes generales

des ondes dans les milieux visqueux et non-visqueux. Ann. Ecole Normale (3) 23, 169-225. Repr. Paris: Gauthier-Villars 1906. (71,90)

[2] JAUMANN, G.: Elektromagnetische Vorgange in bewegten Medien. Sitzgsber. Akad. Wiss. Wien (Ila) 15, 337-390. (19A)

[3] PRANDTL, L.: Zur Theorie des VerdichtungsstoBes. Z. ges. Turbinenwesen 3, 241-245= Ges. Abh. 2, 935-942. (96t)

1907 [1] COSSERAT, E. and F.: Sur la mecanique generale. C. R. Acad. Sci. Paris 145, 1139-1142. (19A,98)

1909 [1] COSSERAT, E., and F.: Theorie des Corps Deformables. Paris: Hermann, vi+ 226pp. Pub!. also as pp. 953-1173 of O. D. CHWOLSON, Traite de Physique, trans!. E. DAVAUX, 2nd ed., 2, Paris 1909. (19A, 98)

[2] POYNTING, J. H.: On pressure perpendicular to the shear-planes in finite pure shears, and on the lengthening of loaded wires when twisted. Proc. Roy. Soc. Lond. A 82, 546-559 = Papers 2, 358-371. (54, 66)

[3] VOLTERRA, V.: Sulle equazioni integro-differenziali della teoria dell'elasticita. Rend. Lincei (5) 181 , 295-301 = Opere 3, 288-293. (41)

[4] VOLTERRA, V.: Equazioni integro-differenziali della elasticita nel caso della isotropia. Rend. Lincei (5) 181' 577-586 = Opere 3, 294-303. (41)

1910 [1] KOTTER, F.: "Uber die Spannungen in einem urspriinglich geraden, durch Einzelkrafte in stark gekriimmter Gleichgewichtslage gehaltenen Stab. Sitzgsber. Preuss. Akad. Wiss. Teil2, 895-922. (60, 66, 86)

[2] VOIGT, W.: Lehrbuch der Kristallphysik. Leipzig u. Berlin: Teubner. (33) 1911 [1] ALMANSI, E.: Sulle deformazioni finite dei solidi elastici isotropi, I. Rend. Accad.

Lincei (5A) 201 , 705-714. (86) [2] ALMANSI, E.: Sulle deformazioni finite dei solidi elastici isotropi, III. Rend.

Accad. Lincei (5A) 202 , 289-296. (86) [3] HOUSTON, R. A.: A relation between tension and torsion. Phil. Mag. (6) 22,

740-741. (86) [4] J AUMANN, G.: Geschlossenes System physikalischer und chemischer Differential

gesetze. Sitzgsber. Akad. Wiss. Wien (Ila) 120, 385-530. (19A, 99) 1912 [1] HAMEL, G.: Elementare Mechanik. Leipzig u. Berlin: Teubner. (42) 1913 [1] HEUN, K.: Ansatze und allgemeine Methoden der Systemmechanik. Enz. math.

Wiss.42 (1904-1935), art. 11. (98) [2] POYNTING, J. H.: The changes in length and volume of an India-rubber cord when

twisted. India-Rubber J., Oct., 4, p. 6 = Papers 2, 424-425. (54, 66) 1914 [1] HELLINGER, E.: Die allgemeinen Ansatze der Mechanik der Kontinua. Enz.

Math. Wiss. 4', 602-694. (42, 68b, 88, 98) 1915 [1] ARMANNI, G.: Sulle deformazioni finite dei solidi elastici isotropi. Nouvo Cimento

(6) 10, 427-447. (44) 1916 [1] ALMANSI, E.: La teoria delle distorsioni e Ie deformazioni finite dei solidi elastici.

Rend. Accad. Lincei (5) 252 , 191-192. (44) 1917 [1] LOHR, E.: Entropieprinzip und geschlossenes Gleichungssystem. Denkschr.

Akad. Wiss. Wien 93, 339-421. (99) 1918 [1] J AUMANN, G.: Physik der kontinuierlichen Medien. Denkschr. Akad. Wiss. Wien

95, 461-562. (99)


1920 [1] ]OUGUET, E.: Sur les ondes de choc dans les corps solides. C. R. Acad. Sci. Paris 171,461-464. (71, 73)

[2] ] OUGUET, E.: Sur la celerite des ondes dans les corps solides. C. R. Acad. Sci. Paris 171,512-515. (71, 73, 77)

[3] ] OUGUET, E.: Sur la variation d'entropie dans les ondes de choc des solides elastiques. C. R. Acad. Sci. Paris 171, 789-791. (71, 73)

[4] ]OUGUET, E.: Application du principe de Carnot-Clausius aux ondes de choc des solides elastiques. C. R. Acad. Sci. Paris 171, 904-907. (71, 73)

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35*


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1945 [1] MURNAGHAN, F. D.: A revision of the theory of elasticity. Bol. Soc. Mat. Mexicana 2, 81-89. (99, 103)

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1946 [1] CATTANEO, C.: Su un teorema fondamentale nella teoria delle onde di discontinuita. Atti Accad. Sci. Lincei Rend., Cl. Sic. Fis. Mat. Nat. (8) 1, 66-72, 728-734. (68b, 71,73)

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1947 [1] BHAGAVANTAM, S., and R. SURYANARAYANA: Third-order elastic coefficients of crystals. Nature, Lond. 160. 750-751. (66)

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Z. angew. Math. Mech. 25/27, 146-150. (111, 113, 119) [4] GARCIA, G.: Ecuaciones exactas y soluciones exactas del moviIniento y de las

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550

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1948 [1]

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[8] KONDO, K.: The mathematical analyses of the yield point, 1. Uniform stress. J. Japan Soc. Appl. Mech. 3, 188-195. (34)

[9] KONDO, K.: Mathematical analyses of the yield point, II. J. Japan Soc. Appl. Mech. 4, 4-8. (34)

[10J LICHNEROWICZ, A.: Elements du Calcul Tensoriel. Paris: Armand Colin. Engl. transl., Elements of Tensor Calculus. New York: John Wiley & Sons. (6)

[11] OLDROYD, J. G.: On the formulation of rheological equations of state. Proc. Roy. Soc. Lond. A 200, 523-541. Reprinted in Rational Mechanics of Materials. IntI. Sci. Rev. Ser. New York: Gordon & Breach 1965. (19A, 36, 37,113,119)

[12] OLDROYD, J. G.: Finite strains in an anisotropic elastic continuum. Proc. Roy. Soc. Lond. A 202, 407-419. (43, 69, 84)

[13] RIVLIN, R. S.: On the definition of strain. Some Recent Developments in Rheology, pp.125-129. London: United Trade Press. (43)

[14] RIVLIN, R. S.: Some flow properties of concentrated high-polymer solutions. Proc. Roy. Soc. Lond. A 200, 168-176. (104)

[15] SIGNORINI, A.: Un semplice esempio di 'incompatibilita' tra la elastostatica classica e la teoria delle deformazioni elastiche finite. Acad. Naz. Lincei Rend. CI. fis. mat. nat. (8) 8, 276-281. (63, 64)

[16] TRUESDELL, C.: A new definition of a fluid, 1. The Stokesian fluid. J. Math. Pures Appl. (9) 29,215-244. (3,13,108,119, 119A, 120, 121)

[17] WEISSENBERG, K.: Rheology of hydrocarbon gels. Proc. Roy. Soc. Lond. A 200, 183-188. (114, 119)

1951 [1] FUMI, F. G.: Third-order elastic coefficients of crystals. Phys. Rev. (2) 83, 1274-1275. (66)

[2] GREEN, A. E., and R. T. SHIELD: Finite extension and torsion of cylinders. Phil. Trans. Roy. Soc. Lond. A 224, 47-86. Reprinted in Problems of Non-linear Elasticity. IntI. Sci. Rev. Ser. New York: Gordon & Breach 1965. (67,70)

[3] GREENSMITH, H. W., and R. S. RIVLIN: Measurements of the normal stress effect in solutions of polyisobutylene. Nature, Lond. 168, 664-667. (115, 116)

[4] ISHIHARA, A., N. HASHITSUME, and M. TATIBANA: Statistical theory of rubber-like elasticity. IV. Two-dimensional stretching. J. Chern. Phys. 19, 1508-1512. (95)

[5] KONDO, K.: Mathematical analyses of the yield point, III. Isotropic stress. J. Japan Soc. Appl. Mech. 4, 35-38. (34)

[6] LODGE, A. S.: On the use of convected coordinate systems in the mechanics of continuous media. Froc. Cambridge Phil. Soc. 47, 575-584. (15)

[7] MOONEY, M.: Secondary stresses in viscoelastic flow. J. Colloid Sci. 6,96-107. (119) [8] MURNAGHAN, F. D.: Finite Deformation of an Elastic Solid. New York: John

Wiley & Sons. (42, 66, 103) [9] OLDROYD, J. G.: The motion of an elastica-viscous liquid contained between

coaxial cylinders, 1. Quart. J. Mech. Appl. Math. 4, 271-282. (36,113,119)


[10] OLDROYD, J. G.: Rectilinear flow of non-Bingham plastic solids and non-Newtonian viscous liquids, II. Proc. Cambridge Phil. Soc. 47, 410-418. (117, 119)

[11] REINER, M.: The theory of cross-elasticity [in Hebrew]. Hebrew Inst. Tech. Sci. Publ. 4,15-30. (43)

[12] REINER, M.: The rheological aspect of hydrodynaInics. Quart. Appl. Math. 8, 341-349. (119)

[13] RIVLIN, R. S.: Mechanics of large elastic deformations with special reference to rubber. Nature, Lond. 167, 590-595. (42)

[14] RIVLIN, R. S., and D. W. SAUNDERS: Large elastic deformations of isotropic materials, VII. Experiments on the deformation of rubber. Phil. Trans. Roy. Soc. Lond. A 243, 251-288. (53, 55, 57, 67, 93, 95)

[15] RIVLIN, R. S., and A. G. THOMAS: Large elastic deformations of isotropic materials, VIII. Strain distribution around a hole in a sheet. Phil. Trans. Roy. Soc. Lond. A 243, 289-298. (60)

[16] SIPS, R.: Propagation phenomena in elastic-viscous media. J. Polymer Sci. 6, 285-293 (96t)

[17] TRUESDELL, C.: A new definition of a fluid, II. The Maxwellian fluid. J. Math. Pures Appl. 30, 111-155. (13, 96, 119, 125)

[18] VIGUIER, G.: Circulation d'un fluide visqueux incompressible. Bull. Acad. Roy. Belg. Cl. Sci. (5) 37, 397-405. (119)

1952 [1] ADKINS, J. E., and R. S. RIVLIN: Large elastic deformations of isotropic materials, IX. The deformation of thin shells. Phil. Trans. Roy. Soc. Lond. A 244, 505-531. (60)

[2] ANDERSSON, B.: On the stress-tensor of viscous isotropic fluids. Ark. Fysik 4, 501-503. (116)

[3] BRAUN, I., and M. REINER: Problems of cross-viscosity. Quart. J. Mech. Appl. Math. 5, 42-53. (114, 119)

[4] FUMI, F. G.: Physical properties of crystals: The direct-inspection method. Acta Cryst. 5, 44-48. (66)

[5] FUM I, F. G.: The direct-inspection method in systems with a principal axis of symmetry. Acta Cryst. 5, 691-695. (66)

[6] FUMI, F. G.: Third-order elastic coefficients in trigonal and hexagonal crystals. Phys. Rev. (2) 86, 561. (66)

[7] GENT, A. N., and R. S. RIVLIN: Experiments on the mechanics of rubber, I. Eversion of a tube. Proc. Phys. Soc. Lond. B 65, 118-121. (57)

[8] GENT, A. N., and R. S. RIVLIN: Experiments on the mechanics of rubber, II. The torsion, inflation, and extension of a tube. Proc. Phys. Soc. Lond. B 65, 487-501. (57)

[9] GENT, A. N., and R. S. RIVLIN: Experiments on the mechanics of rubber, III. Small torsion of stretched prisms. Proc. Phys. Soc. Lond. B 65, 645-648. (70)

[10] GRAD, H.: Statistical mechanics, thermodynamics, and fluid dynamics of systems with an arbitrary number of integrals. Comm. Pure Appl. Math. 5, 455-494. (98)

[11] GREEN, A. E., R. S. RIVLIN, and R. T. SHIELD: General theory of small elastic deformations superposed on finite elastic deformations. Proc. Roy. Soc. Lond. A 211, 128-154. (68, 69, 70)

[12] GREENSMITH, H. W.: Flow Properties of High Polymers. Thesis, Univ. London. (115,116)

[13] KONDO, K.: On the geometrical and physical foundation of the theory of yielding. Froc. 2nd Japan Congr. Appl. Mech. pp. 41-47. (34)

[14] MARKOVITZ, H. : A property of Bessel functions and its application to the theory of two rheometers. J. Appl. Phys. 23, 1070-1077. (113)

[15] REINER, M.: A possible cross-viscosity effect in air. Bull. Res. Council Israel 2, 65. (119)

[16] RICHTER, H.: Zur Elastizitatstheorie endlicher Verformungen. Math. Nachr. 8, 65-73. English transl. in Foundations of Elasticity Theory. Inti. Sci. Rev. Ser. New York: Gordon & Breach 1965. (42, 43, 47)

[17] RIVLIN, R. S., and D. W. SAUNDERS: The free energy of deformation for vulcanised rubber. Trans. Farady Soc. 48, 200-206. (55)

[18] RIVILIN, R. S., and A. G. THOMAS: Rupture of rubber,!. Characteristic energy for tearing. J. Polymer Sci. 10, 291-318. (83)

[19] ROBERTS, J. E.: The pressure distribution in liquids in laminar shearing motion and comparison with predictions from various theories. British Ministry of Supply Report, August. (115, 116)

[20] TRUESDELL, C.: The mechanical foundations of elasticity and fluid dynamics. J. Rational Mech. Anal. 1, 125-300. Corrected reprint, IntI. Sci. Rev. Ser.


New York: Gordon & Breach 1965. (4,5. 19A, 28.42,45,53,54,56,64,66,68,82, 82A, 84, 85, 86, 87, 88, 89, 94, 95,98,104, 108, 115, 119, 119A, 120, 121,125)

[21] TRUESDELL, C.: Review of MURNAGHAN [1951,8]. Bull. Amer. Math. Soc. 58,577-579. (103)

[22] TRUESDELL, C.: A program of physical research in classical mechanics. Z. angew. Math. Phys. 11, 79-95. Reprinted along with [1952,20], Inti. Sci. Rev. Ser. New York: Gordon & Breach. 1965. (28,108, 119A, 120)

[23] WANG, M. C., and E. GUTH: Statistical theory of networks of non-Gaussian flexible chains. J. Chem. Phys. 20,1144-1157. (95)

1953 [1] ADKINS, J. E., A. E. GREEN, and R. T. SHIELD: Finite plane strain. Phil. Trans. Roy. Soc. Lond. A 246, 181-213. (57,59,60)

[2] BODASZEWSKI: 0 niesymetrycznym stanie napie\(ia i 0 jego zastosowaniach w mechanice osrodk6w cil\glych. Arch. Mech. Stosow. 5,351-396. (This work is characterized by KALISKI, I'l.OCHOCKI, and ROGULA [1962, 39] as "absolutely incorrect". )

[3] BORDONI, P. G.: Sopra Ie trasformazioni termoelastiche finite di certi solidi omogenei ed isotropi. Rend. Mat. e Applic. (5) 12, 1-30. (94)

[4] BORDONI, P. G.: Deduzione di un'equazione di stato dei solidi dalla teoria delle trasformazioni termoelastiche finite. Rend. Accad. Lincei (8) 14, 784-790. (94)

[6] BORDONI, P. G.: Trasformazioni adiabatiche di ampiezza finita. Ricerca Sci. 23, 1569-1578. (94)

[6] ERICKSEN, J. L.: On the propagation of waves in isotropic incompressible perfectly elastic materials. J. Rational Mech. Anal. 2, 329-337. Reprinted in Problems of Non-linear Elasticity. IntI. Sci. Rev. Ser. New York: Gordon & Breach 1965. (48,49, 72, 78, 95)

[7] GILBARG, D., and D. PAOLUCCI: The structure of shock waves in the continuum theory of fluids. J. Rational Mech. Anal. 2, 617-642. (119)

[8] GREEN, A. E., and E. W. WILKES: A note on the finite extension and torsion of a circular cylinder of compressible elastic isotropic material. Quart. J. Mech. AppI. Math. 6, 240-249. (66)

[9] GREENSMITH, H. W., and R. S. RIVLIN: The hydrodyna!nics of non-Newtonian fluids, III. The normal stress effect in high-polymer solutions. Phil. Trans. Roy. Soc. Lond. A 245, 399-429. (115, 116, 119)

[10] GUMBRELL, S. M., L. MULLINS, and R. S. RIVLIN: Departures of the elastic behaviour of rubbers in simple extension from the kinetic theory. Trans. Faraday Soc. 49,1495-1505.(95)

[11] HEARMON, R. F. S.: "Third-order" elastic constants. Acta Crystal. 6, 331-339. (66) [12] HERMANS, J. J.: Dilute solutions of flexible chain molecules. Flow Properties of

Disperse Systems, pp. 199-265. Amsterdam: North Holland Publ. Co. (113) [13] HUGHES, D. S., and J. R. KELLY: Second-order elastic deformation of solids.

Phys. Rev. (2) 92, 1145-1149. (66, 76, 77) [14] KRIEGER, I. M., and H. ELROD: Direct determination of the flow curves of non

Newtonian fluids, II. Shearing rate in the concentric cylinder viscometer. J. Appl. Phys.27, 134-136. (113)

[15] LEE, E. H., and I. KANTER: Wave propagation in finite rods of viscoelastic materials. J. Appl. Phys. 24,1115-1122. (96t)

[16] MANACORDA, T.: Sullegame sforzi-deformazione nelle trasformazioni finite di un mezzo continuo isotropo. Riv. Mat. Univ. Parma 4, 31-42. (47)

[17J MISICU, M.: Echilibrul mediilor continue cu deformari mario Stud. Cercet. Mec. Metal. 4, 31-53. (42, 63, 68b)

[18J MOONEY, M.: A test of the theory of secondary viscoelastic stress. J. Appl. Phys. 24, 675-678. (119)

[19J NIORDSEN, F.: Andliga deformationer inom elasticitetsterion. lnst. Hallfasthetslara Kungl. Tekn. Hogskolen Stockholm, Publ. nr. 106. (42)

[20] NOVOZHILOV, V. V.: Foundations of the Nonlinear Theory of Elasticity. Translated by F. BAGEMIHL, H. KOMM, and W. SEIDEL from a Russian book published in 1948. Rochester: Graylock. (42)

[21J NYE, J. F.: Some geometrical relations in dislocated crystals. Acta Metallurg. 1,153-162. (34)

[2g] PAWLOWSKI, J.: Bestimmung des Reibungsgesetzes dernicht-Newtonschen Fliissigkeiten aus den Viskositiitsmessungen !nit Hilfe eines Rotationsviskosimeters. Kolloid-Z. 130, 129-131. (113)

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1955 [1] ADKINS, J. E.: Finite deformation of materials exhibiting curvilinear aeolotropy. Proc. Roy. Soc. Land. A 229,119-134. (34,58,59)

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[4] ADKINS, J. E., and R. S. RIVLIN: Large elastic deformations of isotropic materials, X. Reinforcement by inextensible cords. Phil. Trans. Roy. Soc. Lond. A 248, 201-223. (30, 43)

[5] BILBY, B. A., R. BULLOUGH, and E. SMITH: Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry. Proc. Roy. Soc. Lond. A 231, 263-273. (34)

[6] BILBY, B. A.: Types of dislocation sources. Defects in crystalline solids. Report of conf. at Bristol, 1954, pp. 123-133. London: The Physical Society. (34)

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[8] COTTER, B., and R. S. RIVLIN: Tensors associated with time-dependent stress. Quart. Appl. Math. 13,177-182. (19A, 36)

[9] DEWITT, T. W.: A rheological equation of state which predicts non-Newtonian viscosity, normal stresses, and dynamic moduli. J. Appl. Phys. 26, 889-894. (113, 115, 119)

[10] ERICKSEN, J. L.: Eversion of a perfectly elastic spherical shell. Z. angew. Math. Mech. 35, 381-385. (57, 64, 95)

[11] ERICKSEN, J. L.: Deformations possible in every compressible, isotropic, perfectly elastic material. J. Math. Phys. 34, 126-128. Reprinted in Problems of Nonlinear Elasticity. IntI. Sci. Rev. Ser. New York: Gordon & Breach 1965. (91)

[12] ERICKSEN, J. L.: A consequence of inequalities proposed by BAKER and ERICKSEN. J. Wash. Acad. Sci. 45, 268. (119)

[13] GREEN, A. E.: Finite elastic deformation of compressible isotropic bodies. Proe. Roy. Soc. Lond. A 227, 271-278. (59)

[14] JAIN, M. K.: Boundary-layer effects in non-Newtonian fluids. Z. angew. Math. Mech. 35, 12-16. (119)

[15] JAIN, M. K.: The motion of an infinite cylinder in rotating non-Newtonian liquid. Z. angew. Math. Mech. 35, 379-381. (119)

[16] KONDO, K., and collaborators: Memoirs of the Unifying Study of the Basic Problems of Engineering Sciences by Means of Geometry, 1. Tokyo: Gakujutsu Bunken Fukyu-Kai. (34)

[17] KROUPA, F.: Plane deformation in the non-linear theory of elasticity. Czechosl. J. Phys. 5, 18-29. (95)

[18] MANACORDA, T.: Sulla torsione di un cilindro circolare omogeneo e isotropo nella teoria delle deformazioni finite di solidi elastici incomprimibili. Boll. Un. Mat. Ital. (3) 10, 177-189. (95)

[19] NOLL, W.: On the continuity of the solid and fluid states. J. Rational Mech. Anal 4, 3-81. Reprinted in Rational Mechanics of Materials. IntI. Sci. Rev. Ser. New York: Gordon & Breach 1965. (19A, 28, 36, 39, 42,43,48,84,85,98,99,100,108,111. 113, 119, 126)

[20J REINER, M.: The complete elasticity law for some metals according to POYNTING'S observations. Appl. Sci. Res. A 5, 281-295. (59)

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[35] PIPKIN, A. C., and R. S. RIVLIN: The formulation of constitutive equations in continuum physics. Div. Appl. Math. Brown Univ. Report. Sept. (11, 13, 29, 33,96,97)

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Addendum.

The following additional papers bear on the subject of the treatise. The italic numbers in parentheses indicate the sections in which reference to the paper would have been made, had we seen it in time.

1951 A NOVOZHILOV, V. V.: The connection between stress and deformation in non-linearly elastic media [in Russian]. Priklad. Mat. Mekh. 15, 184-194. (47, 85)

1963 A RATHNA, S. L., and P. L. BHATNAGAR: Weissenberg and Merrington effects in nonNewtonian fluids. J. Indian Inst. Sci. Bangalore 45, 57-82. (123)

1964 A DUVAUT, G.: Lois de comportements pour un milieu isotrope materiellement polarise de degre 2. C. R. Acad. Sci. Paris 259, 3178-3179. (98)

B FINZI, L.: Sulle equazioni costitutive nella meccanica dei continui. 1st. Lombardo Rend. Sci. A 97 (1963), 644-649. (26)

C GRIOLI, G.: Sulla meccanica dei continui a trasformazioni reversibili con caratteristiche di tensione asimmetriche. Sem. 1st. Naz. Alta Mat. 1962-3, 535-555. (98)

D MINDLIN, R. D.: On the equations of elastic materials with micro-structure. Columbia Univ. Dept. Civil Engr. Rep. No. 51, June. (98)

E MINDLIN, R. D.: Stress functions for a Cosserat continuum. Columbia Univ. Dept. Civil Engr. Rep. No. 53, September. (98)

F TANNER, R. 1.: Observations on the use of Oldroyd-type equations of state for viscoelastic liquids. Chern. Engr. Sci. 19, 349--355. (119)

1965 A BLAND, D. R.: On shock structure in a solid. J. Inst. Maths Applics I, 56-75. (74) B BLEUSTEIN, J. L.: Effects of micro-structure on the stress concentration at a

spherical cavity. Columbia Univ. Dept. Civil Engr. Rep. No. 54, February. (98) C BOGARDUS, E. H.: Third-order elastic constants of Ge, MgO, and fused Si02 · J.

Applied Phys. 36, 2504-2513. (63) D BROWN, W. F.: Basis of a rigorous theory of magnetostriction. Proc. IntI. Conf.

Magnetism (Nottingham, 1964). (97) E BROWN, W. F.: Theory of magnetoelastic effects in ferromagnetism. J. Applied

Phys. 36, 994-1000. (97) F COLEMAN, B. D., and M. E. GURTIN: Thermodynamics and one-dimensional shock

waves in materials with memory. Submitted for publication. (71, 96t) G COLEMAN, B. D., and V. J. MIZEL: On the existence of a caloric equation of state.

Proc. 4th IntI. Congr. Rheoi. 1963,3, 34-36. (96) H DAVISON, L. W.: Propagation of finite amplitude waves in elastic solids, Thesis,

Calif. Inst. Tech. (71, 74) I ERINGEN, A. c., and J. D. INGRAM: A continuum theory of chemically reacting

media. IntI. J. Engr. Sci. 3, 197~212. (130) ] ESHEL, N. N.: Effects of strain-gradient on stress-concentration at a cylindrical

hole in an elastic solid. Columbia Univ. Dept. Civil Engr. Rep. No.2, June. (98) K GIESEKUS, H.: Some secondary flow phenomena in general visco-elastic fluids. Proc.

4th IntI. Congr. Rheoi. 1963, 1, 249-266. (123) L GIESEKUS, H.: Sekundarstromungen in viskoelastischen Fliissigkeiten bei statio

narer und periodischer Bewegung. RheoI. Acta 4, 85-101. (122, 123) M GINN, R. F., and A. B. METZNER: Normal stresses in polymeric solutions. Proc.

4th IntI. Congr. RheoI. 1963, 2, 583-602. (116) N GREEN, A. E.: A note on linear transversely isotropic fluids. Mathematika 12,

27-29. (126) o GREEN, A. E., and P. M. NAGHDI: Plasticity theory and multipolar continuum

mechanics. Mathematika 12, 21-26. (5, 98) P HAYES, J. W., and R. 1. TANNER: Measurements of the second normal stress dif

ference in polymer solutions. Proc. 4th IntI. Congr. Rheo!. 1963, 3, 389--399. (112) Q JOHN, F.: Estimates for the derivatives of the stresses in a thin shell and interior

shell equations. Comm. Pure Appi. Math. 18, 235--267. (94) R LIANIS, G.: Small deformation superposed on an initial large deformation in visco

elastic bodies. Proc. 4th IntI. Congr. RheoI. 1963, 2, 109-119. (41)

Addendum. 579

S LOCKETT, F. J.: Creep and stress-relaxation experiments for non-linear materials. IntI. J. Engr. Sci. 3, 59-75. (41)

T MARKOVITZ, H., and B. D. COLEMAN: Nonsteady helical flow of second-order fluids. Proc. 4th IntI. Congr. RheoI. 1963, 2, 143-145. (123)

U MILLER, C. E., and W. H. HOPPMAN II: Velocity field induced in a liquid by a rotating cone. Proc. 4th IntI. Congr. RheoI. 1963, 2, 619-636. (123)

V MINDLIN, R. D.: Second gradient of strain and surface-tension in linear elasticity. Columbia Univ. Dept. Civil Engr. Rep. NO.1, March. (98)

W MORGAN, A. J. A.: On the construction of constitutive equations for continuous media. Arch. Mech. Stosow. 17, 145-174. (26)

X NARASIMHAN, M. N. L.: Stability of flow of a non-Newtonian liquid between two rotating cylinders in the presence of a circular magnetic field. Proc. 4th IntI. Congr. RheoI. 1963, 1, 345-363. (119)

Y PIPKIN, A. C.: Some non-Newtonian effects in flow through tubes. Proc. 4th IntI. Congr. RheoI. 1963, 1,213-222. (122)

Z PIPKIN, A. C., and R. S. RIVLIN: Mechanics of rate-independent materials. Z. angew. Math. Phys. 16, 313-326. (5)

AA PIPKIN, A. C., and M. SINGH: Controllable states of elastic dielectrics. Arch. Rational Mech. Anal., in press. (91, 97)

BB RAMAKANTH, J.: Some problems of propagation of waves in prestressed isotropic bodies. Proc. Vibration ProbI. 6, 161-172. (73)

CC REINER, M.: Second-order stresses in the flow of gases. Proc. 4th IntI. Congr. RheoI. 1963,1,267-279. (116)

DD REINER, M.: Research on second order effects in the elastic response of metals. Technion Found. Report. (70)

EE RIVLIN, R. S.: Nonlinear viscoelastic solids. SIAM Review 7, 323-340. (28,37) FF SEWELL, M. J. : On the calculation of potential functions defined on curved boundaries.

Proc. R. Soc. London A 286, 402-411. (88) GG SHERTZER, C. R., and A. R. METZNER: Measurement of normal stresses in visco

elastic materials at high shear rates. Proc. 4th IntI. Congr. RheoI. 1963,2,603-618. (113)

HH VARLEY, E.: Simple waves in general elastic materials. Arch. Rational Mech. Anal., in press. (74)

II WANG, C.-C.: A representation theorem for the constitutive equation of a simple material in motions with constant stretch history. Arch. Rational Mech. Anal., in press. (109)

37*

Sachverzeichnis. (Deutsch-Englisch. )

Bei gleicher Schreibweise in beiden Sprachen sind die Stichworter nur einmal aufgefiihrt.

Absorption von Wellen, absorption of waves 276.

adiabatisch s. isentrop, adiabatic see isentropic. adiabatische Stabilitat, adiabatic stability 330. Adkinscher Reziprozitatssatz, Adkins'

reciprocal theorem 207. .Aquiprasenzprinzip, equipresence principle

359f., 364. .Aquivalenz von Bewegungen und Vorgangen,

equivalence of motions and processes 42, 43-45·

.Aquivalenzsatz von COSSERAT und TOUPIN, equivalence theorem of Cosserat- Toupin 395.

- fiir Wellen hoherer Ordnung, for higherorder waves 273.

Airysche Spannungsfunktion, Airy's stress function 204.

akustische Achsen, acoustical axes 268, 414. akustischer Tensor, acoustical tensor 268. - -, Symmetrie, symmetry 384. Amplitude einer Welle, amplitude of wave 268,

283. anholonome Komponenten, anholonomic

components 1 5. anisotrope Fliissigkeiten von COLEMAN,

anisotropic fluids of Coleman 88. - - von ERICKSEN, of Ericksen 523-537.

- (fliissige Kristalle), (liquid crystals) 86-88, 151. -, gespeicherte Energie, stored energy 315· - von GREEN, of Green 521-523. -, Hyperelastizitat, hyperelasticity 314 bis 316. --, Stromungsprobleme, flow problems 473-475. - von WANG, of Wang 86-88, 151, 314-316, 473-475.

anisotroper Festkorper, aeolotropic solid 82. - -, gespeicherte Energie, stored energy 312. Anisotropie, aeolotropy 197. -, krummlinige, curvilinear 91. Arbeitsleistung bei einer homogenen De-

formation, work done during a homogeneous deformation 299.

Arbeitssatze fiir elastische Substanzen, work theorems for elastic materials 304-307.

- der Hypoelastizitatstheorie, in hypoelasticity 411-413.

astatische Belastung, astatic load 127.

Aufweitung eines Rohres, inflation of a tube 189---195, 211 f., 343 f., 353.

Ausbreitungsbedingung, propagation condition 268.

Ausbreitungsgeschwindigkeit, propagation speed 268.

-, Effekte zweiter Ordnung, second-order effects 288-291.

Auswirkungsfunktion, response function 296 . - einer elastischen Substanz, of an elastic

material 11 9. -, hypoelastische, hypo-elastic 404 . Auswirkungsfunktional, response functional

36, 58, 61. Axialschwingungen von Fliissigkeiten zwei

ten Grades, axial oscillations of secondgrade fluids 509 f.

Baker-Ericksensche Ungleichungen, B-E inequalities 158-171, 175, 183,281,293.

Basisvektoren, basic vectors 14f., 23. Bernsteinscher Wellensatz, Bernstein's

theorem on waves 332. Beschleunigungsfeld, acceleration field 39. Beschleunigungsgradienten, acceleration

gradients 54. Beschleunigungswellen, Anwachsen und Zer

fall, acceleration waves, growth and decay 384.

- in hypoelastischen Substanzen, in hypoelastic materials 413-415.

- s. auch Wellen, see also waves 267-272. Betrag eines Tensors, magnitude of a tensor

15. Bettischer Satz, Betti's theorem 324f. Bewegung eines Korpers, allgemeine Be

schreibung, motion of a body, general description 38.

Bewegungsgleichungen fiir iiberlagerte infinitesimale Verriickungen, differential equations of motion with superimposed infinitesimal displacement 247.

Bezeichnungen, notations 13-16. bezugsindifferente Grii/3e, frame-indifferent

quantity 42. Bezugsindifferenz, materielle, frame-indif

ference, material 12, 36, 42, 44f., 296. Bezugskonfiguration, reference configuration

48. Bezugssystem, Wechsel, change of frame 41, Biegung, bending 186, 194, 211.

Sachverzeichnis. 581

Biegung eines Blocks, bending of a block 186-188, 211, 342f.

Block, Biegen und Dehnen, block, bending and stretching 186-188, 211, 342.

Boltzmannsche Theorie der Viskoelastizitat, Boltzmann's theory of visco-elasticity 116.

Bordonis spezielle Elastizitatstheorie, Bordoni's special theory of elasticity 348.

Bressanscher Wellensatz, Bressan's theorem on waves 282.

Brillouinsche elastische Koeffizienten zweiter Ordnung, Brillouin's coefficients of secondorder elasticity 230.

Brillouinsches Prinzip, Brillouin's principle 360.

Capriolischer Arbeitssatz, Caprioli's work theorem 305.

Cauchyscher Darstellungshauptsatz, Cauchy's basic representation theorem 29.

Cauchy-Greensche Tensoren, Cauchy-Green tensors 53.

CFT 2. Christoffelsche Symbole, Christoffel symbols

19f. Clausius-Duhemsche Ungleichung, Clausius

Duhem inequality 295, 361, 363f. Coleman-Nollsche Bedingung, C-N condition

157,321,333. Coleman-Nollsche CN+-Bedingung, CN+ con

dition 323. Coleman-Nollsche Theorie des schwindenden

Gedachtnisses, Coleman and Noll's theory of fading memory 101-117.

Coleman-Nollsche Ungleichung, Coleman and Noll's inequality 319--324.

Coleman-Nollscher Stabilitatssatz, Coleman and Noll's stability theorem 330.

Colemansche Thermodynamik einfacher Substanzen, Coleman's thermodynamics of simple materials 363-381.

Colemanscher Arbeitssatz, Coleman's work theorem 306.

Couette-Stromung, Couette flow 449£., Coulombsche Experimente tiber Torsion,

Coulomb's experiments on torsion 236. Cosseratsche Substanz, Cosserat material 397. Cosseratsche Theorie polarer elastischer Sub

stanzen, Cosserat's theory of polar elastic materials 389f.

Darstellung einer Funktion, die selbst ein Vektor ist, representation of a vectorvalued function 35. des Gradienten einer Invariante, of the gradient of an invariant 34.

Darstellungshauptsatz von CAUCHY, basic representation theorem of Cauchy 29.

Darstellungssatz fUr isotrope Tensorfunktionen, representation theorem for isotropic tensor functions 32. fUr lineare isotrope Tensorfunktionen, for linear isotropic tensor functions 33. fUr Tensorinvarianten, for tensor invariants 28.

Da Silvascher Drehmomentensatz, Da Silva's theorem on torques 128.

definiter Warmeleiter, definite conductor of heat 384.

Deformation, lokale, deformation, local 52. Deformationen, die moglich sind in allen in

kompressiblen elastischen Korpern, deformations possible in all incompressible elastic bodies 337-342.

-, die moglich sind in allen kompressiblen elastischen Korpern, possible in all compressible elastic bodies 171-179, 336f.

Deformationsfunktion, relative, deformation function, relative 49.

Deformationsgradient, deformation gradient 49.

Deformationstensor s. Deformationsgradient, tensor of deformation see deformation gradient.

Dehnung, gleichmaBig fortschreitende, steady extension 76, 472f. einer hypoelastischen Substanz, extension of hypoelastic material 417 f. und Torsion, gegenseitige Beziehung, and torsion interrelated 264 f.

Dehn ungs- Spannungs-U ngleichungen, E -T inequalities (extension-tension) 157.

Determinante eines Tensors, determinant of a tensor 15, 23f.

- -, ihr Gradient, its gradient 25. Determinismus, determinism 12, 36, 56. Dichte der Masse, density of mass 38. Diffusion, Rahmentheorie, diffusion, frame-

work of theories 537-541. Dilatation, gleichfOrmige, dilatation, uniform

173. - einer hypoelastischen Substanz, of hypo

elastic material 416. Dilatationsgruppe, dilatation group 86. Dimensionsinvarianz, dimensional invariance

64-65· Direktoren eines orientierten Mediums, di

rectors of an oriented medium 389, 392. Dispersion von Wellen, dispersion of waves

276. Dissipationsprinzip, dissipation principle 295. Drehimpuls, moment of momentum 40. Drehgeschwindigkeitstensor, spin tensor 54. Drehmoment in der Couette-Stromung, torque

in Couette flow 449. - bei Stromung zwischen Kegel und Platte,

in cone-and-plate flow 463. Drehschwingungen von Fltissigkeiten zweiten

Grades, angular oscillations of second-grade fluids 510.

Drehungstensor, rotation tensor 52. Druck, pressure 149. -, EinfluB auf Wellengeschwindigkeit, effect

on wave speed 284f. Druck-Kompressions-Ungleichung, P-C in

equality (pressure-compression) 1 55. Duhemsche Identitat fUr akustische Tensoren

Duhem's identity for acoustical tensors 335. Duhemscher Satz tiber Wellen, Duhem's

theorem on waves 272.

582 Sachverzeichnis.

Duhemscher Satz iiber Wellengeschwindigkeiten, Duhem's theorem on wave speeds 335·

Durchsatz bei Kanalstromung, volume discharge in channel flow 444. bei Poiseuille-Stromung, of Poiseuille flow 452. bei Stromung zwischen koaxialen Rohrleitungen, in flow between coaxial pipes 451-

dyadisches Produkt zweier Vektoren, dyadic product of two vectors 15.

ebene infinitesimale Wellen, plane infinitesimal waves 273-278.

ebene Probleme der Elastizitatstheorie, plane problems in elasticity 204-208.

- - - zweiter Ordnung, in second-order 246.

Effekte zweiter Ordnung in isotropen hyperelastischen Substanzen, second-order effects in isotropic hyperelastic materials 344-346.

Eindeutigkeit, ihr Versagen, uniqueness, its failure 128f.

Eindeutigkeitssatz von ERICKSEN und TouPIN, uniqueness theorem of Ericksen and Toupin 255. fUr freie Schwingungen, for free vibrations 256. fiir Potentialdeformationen, for potential deformations 165. von SIGNORINI, of Signorini 225. von TRUESDELL und TOUPIN, of Truesdell and Toupin 249.

eindimensionale Probleme, one-dimensional problems 10.

einfache Dehnung, simple extension 173, 180. einfache Festkorper, simple solids 78, 81-86. einfache Fliissigkeiten, simple fluids 13, 78,

79-81, 427-513. einfache Scherbewegung, simple shearing

442f. einfache Scherstromung in Fliissigkeiten

zweiten Grades, simple shearing of second-grade fluids 506.

einfache Scherung elastischer Korper, simple shear of elastic bodies 174.

einfache Substanz, simple material 36, 60 bis 63, 78. - der Ordnung n, of order n 109. -, thermisches Gleichgewicht, thermal equilibrium 298-301-

einfache Substanzen, Grundeigenschaften, simple materials, basic properties 66-69.

Einheitstensor, unit tensor 23 elastische anisotrope Fliissigkeit, elastic sub

fluid 151-elastische Dielektrika, elastic dielectrics 385 bis

388. elastische Effekte zweiter Ordnung, second

order effects in elasticity 229--246. elastische Fliissigkeit, elastic fluid 148.

-, gespeicherte Energie, stored energy 313.

elastische Konstanten zweiter Ordnung, Bestimmung aus Wellengeschwindigkeiten, second-order elasticities, determination by wave speeds 290f.

elastische Stabilitat, elastic stability 252-260. elastisohe Su bstanz, elastic material 106, 11 7. - -, Definition, its definition 13, 117, 119f.

-, Isotropiegruppe, isotropy group 122. - als Naherung, as approximation 111. -, polare, polar 389--401--, verstarkte, reinforced 122.

elastische Theorien der Fliissigkeiten, elastic theories of fluids 480 f.

elastischer Festkorper, elastic solid 149, 170. elastischer Korper, elastic body 125. Elastizitat hoherer Ordnung, Experimentel-

les, higher-order elasticities, experimental 230.

-, klassische infinitesimale Theorie, classical infinitesimal theory 117.

- n-ter Ordnung, of n-th order 228. -, reduzierte Materialgleichungen, reduced

constitutive equations 113, 120f. Elastizitatskoeffizienten, Anzahl unabhan

giger, elasticities, number of independent ones 309f. einer elastischen Substanz, of an elastic material 132.

-, scheinbare, apparent 239f., 251 f. Elastostatik, Differentialgleichung, elasto

statics, differential equation 127. - einfacher Substanzen, of simple materials

123. Elektrizitat und Warme, Analogie, electricity

and heat, analogy 388. elektromechanische Theorien, electromechani

cal theories 385-389. elliptisches Rohr, sekundare Stromung,

elliptical tube, secondary flow 503. endliche elastische Deformation, Bewegungs

gleichung, finite elasticity, differential equation of motion 125.

Energiebilanz, energy balance 294f. Energiefunktional, energy functional 298. Entropie, entropy 133, 294f. Entropiebeziehung, entropy relation 302, 368. Entropieerzeugung, production of entropy 295. Entropiefunktion, entropy function 301. Entropieungleichung, entropy inequality 295,

357. Ereignis (= Weltpunkt), event (= point in

space-time) 41-Ericksensche anisotrope Fliissigkeiten, Erick

sen's anisotropic fluids 523-537. Ericksenscher Arbeitssatz, Ericksen's work

theorem 307. ERICKSENS Untersuchung der moglichen De

formationen in allen inkompressiblen elastischen Korpern, Ericksen's analysis of deformations possible in aU incompressible elastic bodies 337-342. - - - in allen kompressiblen elastischen Korpern, in aU compressible elastic bodies 336f.


Erinnerung an die Vorgeschichte, recollection of a history 102.

Erinnerungsvermogen s. Gedachtnis, memory. Euklidische Invarianz, Euclid invariance 392,

395· Euklidische Wirkung, Euclidean action 389,

392. E-Ungleichungen, E-inequalities 171. Existenz- und Eindeutigkeitssatze der Elasti

zitatstheorie, existence and uniqueness theorems in elasticity 133-139.

FlieBbewegung anisotroper Festkorper, flow of anisotropic solids 520-523.

FlieBen in der Hypoelastizitatstheorie, yield in hypoelasticity 420-426.

fltissige Kristalle, liquid crystals (subfluids, anisotropic fluids) 86-88, 151, 314-316, 473-475, 523-537.

Fltissigkeiten, einfache, fluids, simple 427 bis 513-erster Ordnung, of first order 100. von geschwindigkeitsabhangiger Struktur, of rate type 482-484.

- -, spezielle Theorien, special theories 475 bis 513. verschiedenen Grades, of different grades 494. verschiedener Ordnung, of different orders 491, zweiten Grades, of second grade 504--513. zweiter Ordnung, of second order 100.

Fluiditat, fluidity 13. Frechetsches Differential, Frichet differential

104. freie Energie, free energy 301. - -, Minimum, minimum 370. freie Oberflachenform, free shape 130. Fresnel-Hadamardscher Satz tiber Wellen-

ausbreitung, Fresnel-Hadamard theorem on wave propagation 168.

Fresnelsche quadratische Form, Fresnel quadric 268.

Fresnelsches Ellipsoid, Fresnel's ellipsoid 332. Fundamentalsatz tiber einfache Substanzen,

fundamental theorem on simple materials 66. von HADAMARD tiber Wellen, of Hadamard on waves 271, 332f. ti ber hyperelastische Festkorper, on hyperelastic solids 311. von NOLL liber einfache Fllissigkeiten, of Noll on simple fluids 81, der Stabilitat, of stability 253.

GCN -Bedingung, GCN condition (generalized Coleman-Noll condition) 162-169, 321,

GCNo-Bedingung, GCNo condition 160. GCN+-Bedingung, GCN+ condition 166, 249,

257, 271, 281, GCNt-Bedingung, GCNt condition 162. Gedachtnis, schwindendes, fading memory

36, 101-106, 365. Gemisch ineinander diffundierender Sub

stanzen, mixture of interdiffusing materials 537-541.

Geradebiegen eines Zylindersektors, straightening of a cylindrical sector 188f., 343.

geradlinige Oszillationsstromung, lineal oscillation flow 444 f.

geradlinige Stromung, lineal flow 429-432, 441-445·

--- - von Fllissigkeiten zweiten Grades, of second-grade fluids 510-513.

Geschichte der Hyperelastizitat endlicher Deformationen, history of finite hyperelasticity 304.

Geschwindigkeit der vVellenausbreitung, speed of wave propagation 268.

--- ----, Effekte zweiter Ordnung, second-order effects 288-291.

Geschwindigkeitsfeld, velocity field 39. Geschwindigkeitsprofil einer Kanalstromung,

velocity profile of channel flow 444. - der Poiseuille-Stromung, of Poiseuille

flow 452. Gibbs-Coleman-Nollscher Stabilitatssatz,

Gibbs, Coleman and Noll's stability theorem 331-

Gibbssche Beziehungen, Gibbs relations 372, 381,

gleichformige Dilatation, uniform dilatation 173.

Gleichgewichtsachse, axis of equilibrium 136, 258.

gleichmaBige Bezugsgesamtheit, uniform reference 89.

Grad einer Fllissigkeit, grade of a fluid 494, 504.

- einer Substanz vom Differentialtyp, of a material of differential type 111.

Gradient einer Tensorfunktion, gradient of a tensor function 24-27.

- eines Vektorfeldes, of a vector field 15. Gradienten der Hauptinvarianten, gradients

of principal invariants 25 f. - von Invarianten, Darstellungen, of in

variants, representations 34. Green-Rivlinsche multipolare Elastizitat,

Green and Rivlin's multipolar elasticity 400f.

Greensche anisotrope Fltissigkeiten, Green's anisotropic fluids 521-523.

Green-St. Venantscher Deformationstensor, Green-St. Venant strain tensor 221.

Grioli-Toupinsche Su bstanz, Grioli- Toupin material 400.

Gummi, experimentelle Ergebnisse, rubber, experimental results 171, 181 f.

-, Theorie von MOONEY and RrvLIN, theory of Mooney and Rivlin 349-354.

Gyrationsvektor, gyration vector 386.

Hadamardsche Ungleichung, Hadamard's inequality 253, 257.

Hadamardscher Fundamentalsatz liber Wellen, Hadamard's fundamental theorem on waves 271, 332f.

Hagen-Poiseuillesche Ausflu13formel, HagenPoiseuille efflUX formula 466.


Hamilton-Cayleyscher Satz, Hamilton-Cayley theorem 26.

Hauptdehnungsgeschwindigkeiten, principal stretchings 472.

Hauptinvarianten eines Tensors, principal invariants of a tensor 23, 25·

Hauptkrafte, principal forces 144, 317. Hauptspannungen, principal stresses 143. Hauptwellen, principal waves 279. --, Fundamentalsatze, fundamental theorems

280f. --, Kompatibilitatsbedingungen, compatibi

lity conditions 286-288. hemitrope Tensorfunktion, hemitropic tensor

function 24. Hemitropie, hemitropy 358. homentrope Wellen, homentropic waves 272,

335,383f. homogene Bewegungen, isochore, homogene

ous motions, isochoric 74. homogene reine Dehnungs-Vorgeschichte,

homogeneous pure-stretch history 66. homogene Stromung der anisotropen Fliissig

keiten von ERICKSEN, homogeneous flow of Ericksen's anisotropic fluids 530-533.

homogene Verzerrung, homogeneous strain 171-183.

homogene Verzerrungs-Vorgeschichte, homogeneous strain history 62.

homogener Korper, homogeneous body 59, 90. Homogenitat der Substanz, Verlust bei Ver

zerrung, homogeneity of material lost by strain 25t.

homotherme Wellen, homothermal waves 272, 335, 383 f.

hydrostatische Spannungszustande in elastischen Substanzen, hydrostatic tension states in elastic materials 170.

hydrostatischer Druck, EinfluB auf Wellengeschwindigkeit, hydrostatic pressure, effect on wave speed 284f.

hyperelastische anisotrope Fliissigkeiten, hyperelastic subfluids 314-316.

hyperelastische Festkorper, Fundamentalsatz, hyperelastic solids, fundamental theorem 311.

hyperelastische Stabilitat, hyperelastic stability 328-332.

hyperelastische Substanz, hyperelastic material 117, 294 ff.

- -, Definition, definition 302. hyperelastische Substanzen, spezielle Eigen

schaften der Uisungen, hyperelastic materials, special properties of solutions 342 bis 344. - zweiten Grades, of second grade 397 bis 400.

Hyperelastizitat, Definition, hyperelasticity, definition 13.

Hyperspannungstensor, hyperstress tensor 395, 398.

hypoelastische Auswirkungsfunktionen, hypoelastic response function 404.

hypoelastische Substanz, Definition, hypoelastic material, definition 401 f.

hypoelastische Wellen, hypo-elastic waves 413 bis 4'[ 5.

hypoelastisches FlieBen, hypo-elastic yield 420--426.

Hypoelastizitat, hypo-elasticity 13, 117, 401 bis 426.

-, Beziehung zur Elastizitat, relation to elasticity 406-411.

ideale Substanz, ideal material 2, 44. Impuls, momentum 40. infinitesimale ebene -Wellen, infinitesimal

plane waves 273-278-infinitesimale Elastizitatstheorie, infinitesi

mal theory of elasticity 117. infinitesimale Stabilitat, infinitesimal

stability 252-260. infinitesimale Verzerrung, die einer gegebenen

Verzerrung iiberlagert ist, infinitesimal strain superimposed upon a given strain 250, 325.

infinitesimale Viskoelastizitat, infinitesimal visco-elasticity 116.

infinitesimaler Verdrehungstensor, infinitesimal rotation tensor 11 5.

infinitesimaler Verzerrungstensor, infinitesi-mal strain tensor 115.

inkompressibel s. auch isochor. Inkompressibilitat, incompressibility 71. inkompressible elastische Korper, Gesamt-

heit der moglichen Deformation, incompressible elastic bodies, all possible deformations 337-342.

inkompressible elastische Substanz, incompressible elastic material 12t.

- - -, homo gene Verformung, homogeneous strain 179-183.

inkompressible isotrope elastische Substanz, incompressible isotropic elastic material, 147f.

inkompressible isotrope Substanz, Elastizitat zweiter Ordnung, incompressible isotropic material, second-order elasticity 241-246.

inkompressible Substanz, Wellenausbreitung, incompressible material, wave propagation 291-294.

innere Energie, internal energy 294. innere Zwangsbedingungen, internal con

straints 69-73. Invariante mehrerer Tensoren (s. auch In

varianten), simultaneous invariant of several tensors (see also invariant) 22, 24, 25, 31.

Invarianten, Darstellung, invariants, re-presentation 27-32.

-, Listen, lists 30f. -, multilineare, multilinear 30. -, polynomiale, polynomial 28-30. - eines Tensors, of a tensor 22f. irreversible Thermodynamik, irreversible

thermodynamics 373. isentrope Elastizitat, isentropic elasticity 133. isochor s. auch inkompressibel. isochore Bewegung, isochoric motion 39, 55.


isochore homo gene Bewegungen, isochoric homogeneous motions 74.

isotherme Elastizitat, isothermal elasticity 133.

isotherme Kreisprozesse, isothermal cyclic processes 372.

isotherme Stabilitat, isothermal stability 330. isotrope elastische Su bstanz, isotropic elastic

material 139. - - -, elastische Koeffizienten, response

coefficients 140f. isotrope hyperelastische Substanz, isotropic

hyperelastic material 313f., 317-319. isotrope inkompressible elastische Substanz,

isotropic incompressible elastic material 147 f.

isotrope Substanz yom Differentialtyp, isotropic material of differential type 94.

- - ,Wellenausbreitung, wave propagation 278-291.

isotrope Substanzen, isotropic materials 78f. isotrope Tensorfunktion, isotropic tensor

function 22-24, 34. - -, Darstellung, representation 32, 34. Isotropie, Definition, isotropy, definition 358. Isotropiegruppe, isotropy group 76-79.

einer elastischen Substanz, of an elastic material 122. hyperelastischer anisotroper Fliissigkeiten, of hyperelastic subfluids 314-316.

Isotropiegruppen hyperelastischer Substanzen, isotropy groups of hyperelastic materials 31 ()----313.

JOHNS spezielle Elastizitatstheorie, John's special theory of elasticity 349.

kalorische Zustandsgleichung, caloric equation of state 298, 361.

Kanalstromung, channel flow 443 f. Kapillaritatstheorie von KORTEWEG, capil

larity theory of Korteweg 513-515. Kelvinsche Effekte, Kelvin effects 176, 236,

345. kinetische Stabilitat, kinetic stability 259. KIRCHHOFFS spezielle Elastizitatstheorie,

Kirchhoff's special theory of elasticity 348. klassische Ungleichungen, C-inequalities

(classical) 153. kleine elastische Deformationen, die groBen

ii berlagert sind, small elastic deformations superimposed on large ones 116-117.

Klettern in stationarer Couette-Stromung, climbing in steady Couette flow 452-455.

Korper, Definition, body, definition 37. -, homogener, homogeneous 59, 90. Kompatibilitatsbedingung, compatibility con-

dition 127. Kompatibilitatsbedingungen fiir Haupt

wellen, compatibility conditions for principal waves 286-288. von TOUPIN und BERNSTEIN, of Toupin and Bernstein 277, 335.

Kompatibilitatssatz von SIGNORINI, compatibility theorem of Signorini 225.

komplementare Deformationsenergie, complementary strain-energy 327.

kompressible elastische Korper, Gesamtheit der moglichen Deformationen, compressible elastic bodies, all possible deformations 171-179, 336f.

kompressibler elastischer Korper, homo gene Verformung, compressible elastic body, homogeneous strain 171-179.

Konfiguration, Definition, configuration, definition 37.

-, lokale, local 52. Konnektion, materielle, material connection

89. konstante Streckvorgeschichte, constant

stretch history 438-440. Kontaktkraft s. auch Spannung, contact

force see also stress 40. Kontinuitatsgleichung, equation of continuity

39. Kontinuumstheorien und molekulare Theo

rien, Vergleich, continuum and molecular theories compared 5.

kontravariante Ableitungen, contravariant derivatives 16.

kontravariante Komponenten, contravariant components 14f.

Koordinaten, materielle und raumliche, coordinates, material and spatial 37, 39.

Koordinatensysteme, co-ordinate systems 19 f. Kortewegsche Theorie der Kapillaritat, Korte

weg's theory of capillarity 513-515. kovariante Ableitungen, covariant derivatives

16. kovariante Komponenten, covariant compo

nents 14f. Krafte und Spannungen, forces and stresses

39-41. Kraftepaardichte, couple density 394. Kreisprozesse, allgemeiner Satz, cyclic pro

cesses, general theorem 381. --. Ungleichungen, inequalities 369f. kreiszylindrische Rohrleitungen, Stromung,

darin, circular pipes, flow in them 448 bis 452.

Kristallklassen, crystal classes 83. Kugelkoordinaten, spherical co-ordinates 20. Kugeln, Radialschwingungen, spheres, radial

oscillations 217-219. Kugelschale, Aufblasen und Umklappen,

spherical shell, inflation and eversion 195, 344.

Lamesche Elastizitatskoeffizienten, Lame coefficients of elasticity 116-117.

Lamesche Viskositatskoeffizienten, Lame coefficients of viscosity 113.

linear viskose Substanz, linearly viscous material 114.

lineare Tensorfunktion, linear tensor function 22,33.

Losungen der Elastizitatstheorie endlicher Deformationen, genaherte, solutions in finite elasticity, approximate 219-267, 347~354.


Losungen der ElastizWitstheorie endlicher Deformationen, exakte, solutions in finite elasticity, exact 171-219.

lokal viskometrische Bewegung, locally visco-metric motion 432.

lokale Ableitung s. raumliche Ableitung. lokale Deformation, local deformation 52. lokale Konfiguration, local configuration 52. lokale Wirkung, Prinzip, local action, prin-

ciple 12, 36, 56. Lokalisierung einer Bewegung, localization of

a motion 51 f. Longitudinalwelle, longitudinal wave 268, 280.

Makrogrol3en in polaren elastischen Substan zen, macroquantities in polar elastic materials 392.

Makromedium, macromedium 391-Massendichte, mass density 38. Massenverteilung, mass distribution 38. Materialgleichung, allgemeine mechanische,

constitutive equation, general mechanical 57-58. einer elastischen Fltissigkeit, of an elastic fluid 149. einer elastischen Substanz, of an elastic material 119. einer hyperelastischen Substanz, of an hyperelastic material 302. einer inkompressiblen isotropen elastischen Substanz, of an incompressible isotropic elastic material 148.

Materialgleichungen, constitutive equations 2, 36,44.

- von COLEMAN, of Coleman 364f. -, dimensionslose, dimensionally reduced

form 65f., 120. flir Substanzen yom Differentialtyp, of differential type materials 93 f. - von geschwindigkeitsabhangiger Struktur, of rate type materials 95.

materielle Koordinaten und Beschreibung, material co-ordinates and description 37, 39.

materielle Zeitableitung, material time derivative 39.

Maximum der Entropie, Satz yom, theorem on maximum entropy 380.

Maxwellsche Fltissigkeit, Truesdellsche Theorie, Maxwellian fluid, Truesdell's theory 515-520.

Mikrogrol3en in polaren elastischen Substanzen, microquantities m polar elastic materials 392, 395.

Mikromedium, micromedium 391. Minimum der freien Energie, Satz yom, theo

rem on minimum free energy 370. - der inneren Energie, Satz yom, theorem

on minimum internal energy 380. mitgefiihrte Spannungsgeschwindigkeit, con

vected stress-rate 96, 97. Moduln, scheinbare, moduli, apparent 239f. Molekulartheorien und Kontinuumstheorien,

Vergleich, molecular and continuum theories compared 5.

Momente eines Tensors, moments of a tensor 23. - -, ihre Gradienten, their gradients 27. Momentenbedingung, moment condition 258. Momentenspannungstensor, couple-stress

tensor 396, 525. monotone Transformation, monotone trans

formation 161-Mooney-Rivlinsche Theorie des Gummis,

Mooney-Rivlin theory of rubber 349-354. multilineare Invarianten, multilinear in

variants 30. multipolare Elastizitat, multipolar elasticity

400f. Mumaghansche elastische Koeffizienten zwei

ter Ordnung, Murnaghan's coefficients of second-order elasticity 230.

nattirliche Einheiten von Elastizitat, Zeitablauf usw., natural units of elasticity, time-lapse etc. 64.

natiirlicher Zustand, natural state 306, 311, 322.

Navier-Stokessche Gleichungen, NavierStokes equations 476.

Navier-Stokessche Theorie der Viskometrie, N avier-Stokes theory of viscometry 113 ff., 467.

neo-Hookesche Theorie der Elastizitat, neoH ookean theory of elasticity 350.

Nichtleiter ftir Warme, non-conductor of heat 384.

Nollscher Satz tiber Stromungen mit konstanter Streckvorgeschichte, Noll's theorem on flows with constant stretch history 438. tiber einfache Fltissigkeiten, on simple fluids 81-tiber einfache Substanzen, on simple materials 66.

Normalspannung, Endeffekte, normal-stress end effects 452-458.

- in der Stromung zwischen Kegel und Platte, normal-stress in cone-and-plate flow 463.

Normalspannungen bei einfacher Scherung, normal stresses in simple shear 175-178.

Normalspannungsdifferenz in der CouetteStromung, normal-stress difference m Couette flow 449. in einer Fltissigkeit zweiter Ordnung, in a second-order fluid 493. in Stromung zwischen gleitenden Zylindem, in flow between sliding cylinders 451. in Stromung zwischen koaxialen Zylindem, in flow between coaxial cylinders 448.

N ormalspannungsfunktion, normal-stress function 436.

-, modifizierte, modified 446.

Obliviator (Einflul3funktion), obliviator (influence function) 102.

Ordnung einer einfachen Substanz, order of a simple material 109. der Elastizitat, of elasticity 228. einer Fltissigkeit, of a fluid 491.


Ordnung einer Substanz vom Integraltyp, order of a material of integral type 99.

orientierte Medien, oriented media 389. orthogonaler Tensor, orthogonal tensor 15.

partieller Gradient einer Funktion von Tensoren, partial gradient of a function of tensors 25.

physikalische Komponenten, physical components 15.

piezokalorischer Effekt, seine Nichtexistenz, piezo-caloric effect, its non-existence 356.

Piola-Kirchhoffsche Spannungstensoren, Piola-Kirchhoff stress tensors 120, 124£., 144, 169, 300, 320.

Plastizitat, plasticity 8, 420. Poiseuille-Stromung, Poiseuille flow 451 f. -- der anisotropen Fliissigkeiten von ERICK

SEN, of Ericksen's anisotropic fluids 536. polare elastische Su bstanzen, polar elastic

materials 389-401. polarer Zerlegungssatz, polar decomposition

theorem 52. Polarisation, elektrische, polarization, elec

trical 385. Polarisationsellipsoid, ellipsoid of polarization

332. polynomiale Invarianten, polynomial in

variants 28-30. Potential, thermomechanisches, potential,

thermo mechanical 299. Potenzreihe von Tensoren, power series of

tensors 21. Poynting-Effekt, Poynting effect 177, 235,

345. Poyntingsche Experimente iiber Torsion,

Poynting's experiments on torsion 237. Poyntingsches Problem, Poynting's problem

193, 352. Prinzip der Aquiprasenz, principle of equi

presence 359£" 364. der Determiniertheit fiir Spannungen, of determinism for stress 56. der materiellen Bezugsindifferenz, of material frame-indifference 36, 44, 296. -, seine Geschichte, its history 45-47. - fiir Substanzen mit Zwangsbedin-gungen, for constrained materials 70. der lokalen Wirkung, of local action 12, 36, 56. des schwindenden Gedachtnisses, of fading memory 36,101, 103f.

Prinzipien fiir das mechanische Verhalten, principles of mechanical behavior 36.

Produkt von Tensoren, product of tensors 15.

Quadratische Form der Polarisation, quadric of polarization 268.

Quasigleichgewichts-Bewegungen inkompressibler Korper, quasi-equilibrated motions of incompressible bodies 208-214.

Radialschwingungen von Zylindern und Kugeln, radial oscillations of cylinders and spheres 214-219,354.

raumliche Koordinaten und Beschreibung, spatial co-ordinates and description 37, 39.

raumliche Zeitableitung, spatial time derivaative 39.

raumlicher Gradient, spatial gradient 39. Randwertprobleme der Elastizitatstheorie,

boundary-value problems of elasticity 125 bis 129. fiir hyperelastische Substanzen, for hyperelastic materials 326.

Raum-Zeit-Kontinuum, space-time 41. reduzierte Materialgleichungen, reduced con

stitutive equations 66-69, 113, 120. REINER, seine grundlegenden Beitrage, basic

contributions of Reiner 9. Reiner-Rivlinsche Fliissigkeiten, Reiner

Rivlin fluids 477-480, 486. Reissnersches Variationsprinzip, Reissner's

variational principle 328. relative Deformationsfunktion, relative de

formation function 49. relativer Cauchy-Greenscher Tensor, relative

Cauchy-Green tensor 53. relativer Deformationsgradient, relative de

formation gradient 49. relativer Drehungstensor, relative rotation

tensor 53. relativer Streckungstensor, relative stretch

tensor 53. Retardierung einer Vorgeschichte, retarda

tion of a history 109. Retardierungsformeln von COLEMAN und

NOLL, retardation formulae of Coleman and Noll 110-111.

Reziprozitatssatz von ADKINS, reciprocal theorem of Adkins 207.

- von BETTI, of Betti 324f. Rheogoniometer von WEISSENBERG, rheo

goniometer of Weissenberg 464. Rheologie, rheology 8. RIVLIN, seine grundlegenden Beitrage, basic

contributions of Rivlin 9. Rivlin-Ericksensche Fliissigkeiten, Rivlin

Ericksen fluids 481 f. Rivlin-Ericksensche Tensoren, Rivlin Erick

sen tensors 54. - -, Verallgemeinerung, generalization 516. Rivlinsche Formel fiir den Torsionsmodul bei

Dehnung, Rivlin's formula for the torsional modulus under extension 192 f.

Rivlinsche Losungen der Elastizitatstheorie, Rivlin's solutions in elasticity 171-197.

Rivlin-Topakoglusche Deutung der Signorinischen Entwicklung, Rivlin and Topakoglu's interpretation of Signorini's expansion 227-229.

Rohre, Dehnen und Biegen, tubes, inflation and bending 189-195, 212f., 343.

-, nicht kreisfiirmiges, Stromung hindurch, non circulartube, flow through it 468 bis 471.

-', Radialschwingungen, radial oscillations 354.

-, sekundare Stromung, secondary flow 497 bis 504.


Rohre, Torsion und Dehnung, tubes, torsion and extension 232-237, 353.

-, verschiedene Deformationen, various deformations 353.

Rohrleitungen, Stromung darin, pipes, flow inside 448-452.

rotierende Zylinder, Stromung dazwischen, rotating cylinders, flow between them 449f.

scheinbare Moduln und Elastizitatskoeffizienten, apparent moduli and elasticities 239f., 251 f.

Scherbewegung, geradlinige, shearing, rectilinear 76.

- einer hypoelastischen Substanz, of hypoelastic material 418-426.

Schergeschwindigkeit, shearing 436. Schergeschwindigkeitsfunktion, shearing

function 436. Scherspannungsfunktion, shear-stress function

436. Scherungsmodul, verallgemeinerter, shear

modulus, generalized 174, 182. schraubenf5rmige Str5mung, helical flow 445

bis 452. Schwell-Effekt am R5hrenausgang, swelling

at exit from a pipe 455-458. schwindendes Gedachtnis, fading memory

36,101-106, 112f., 365. Schwingungen von Fliissigkeiten zweiten

Grades, oscillations of second-grade fluids 509f.

-, infinitesimale, Eindeutigkeitssatz, infinitesimal, vibrations, uniqueness theorem 256.

S-E-Bedingung (starke Elliptizitat), S-E condition (strong ellipticity) 129, 132, 147, 168f., 248, 254, 271, 281, 333.

sekundare Str5mung, secondary flow 463 f. - - in Rohren, in tubes 497-504. SIGNORINIS spezielle Elastizitatstheorie, Sig-

norini's special theory of elasticity 348. Signorinische Entwicklung, Signorini's ex

pansion 219--227. Spannung, stress 39f. Spannungsbeziehung, stress relation 297, 300

bis 302, 313, 368. - -, Umkehrung, inversion 327. Spannungs-Dehnungs-U ngleichungen, T -E

inequalities (tension-extension) 155. Spannungs-Entropie-Beziehung, stress

entropy relation 367f. Spannungsentropie-Tensor, stress-entropy

tensor 365. Spannungshauptachsen, stress, principal axes

142. Spannungsprinzip, stress principle 40. Spannungsrelaxation, stress relaxation 47,

106f., 369. Spannungsrelaxationsfunktion, stress

relaxation function 115. -, Colemanscher Satz, Coleman's theorem 378. Spannungstensor, mitgefiihrter, stress tensor,

convected 67. -, unsymmetrischer, non symmetrical 389.

Spannungsvektor, stress vector 40. Spannungs-Verformungs-Beziehung, stress

strain relation 119. Speicherenergie, stored energy 302, 312. Speicherenergie-Funktion, stored-energy func

tion 302, 312f., 315. -, konvexe, convex 322. Spencer-Rivlinscher Satz iiber Tensor

invarianten, Spencer-Rivlin theorem on tensor invariants 31-

spezielle Theorien der Elastizitat, special theories of elasticity 347-354.

Sprungfortsetzung, jump continuation 374. Spur eines Tensors, trace of a tensor 15, 23 f. - -, ihr Gradient, its gradient 25. Stabilitat, stability 153. -, elastische, elastic 252-260. - hyperelastischer Korper, of hyperelastic

bodies 328-332. -, kinetische, kinetic 259. Stabilitatssatz von HADAMARD, stability

theorem of Hadamard 253. Starrheit, rigidity 72. Statik der anisotropen Fliissigkeiten von

ERICKSEN, statics of Ericksen's anisotropic fluids 528-530.

statische Fortsetzung, statical continuation 106, 369, 371-

statische Stabilitat, statical stability 328. stoffgleicher elastischer K5rper, materially

uniform elastic body 126. Stoffgleichheit eines K5rpers, material uni-

formity of a body 59, 90. Stoffisomorphie, material isomorphism 59. Stoffkonnektion, material connection 89. Stokessche Fliissigkeit, Truesdellsche Theorie

Stokesian fluid, Truesdell's theory 485 bis 488.

Stokessches Viskositatsprinzip, Stokes's principle of viscosity 475 f.

Stoppellischer Satz, Stoppelli's theorem 138. Stol3welle, shock wave 267. Streckgeschwindigkeitstensor, stretching

tensor 54. Strecktensoren, rechter und linker, stretch

tensors, right and left 53. Streckung eines Zylinders durch Verdrehen,

extension of a cylinder by twisting 193, 352.

Streckvorgeschichte, konstante, constant stretch history 438-440.

Str5mung von anisotropen Fliissigkeiten, flow of subfluids 473-475.

- zwischen Kegel und Platte, cone-andplate flow 461-464. zwischen koaxialen Zylindern, flow between coaxial cylinders 446-452. zwischen rotierenden parallelen Platten, between rotating parallel plates 458-464.

Strukturtheorien und Kontinuumstheorien, Vergleich, structural and continuum theories compared 5.

ST. VENANTS spezielle Elastizitatstheorie, St. Venant's special theory of elasticity 348.

substantiell s. materiell.


Substanzfunktionale, material functionals 431,

Substanz vom Differentialtyp, material of differential type 93-95, 111, gemischten Integral-Differentialtyps, of mixed integral-differential type 101, vom Grad n (s. auch Grad), of grade n (see also grade) 63. von geschwindigkeitsabhangiger Struktur, of rate type 95-98. vom Integraltyp, of integral type 98-101,

Symbole, Verzeichnis, index of symbols 17 bis 19.

Teilchen, Definition, particles, definition 37. Temperatur, temperature 133, 294. Temperaturbeziehung, temperature relation

297, 301, 361, Tensoriunktion, Definition, tensor function,

definition 21, '-, lineare, linear 22, 33. -, multilineare, multilinear 22, 34f. -- einer Variablen, of one variable 32-35. Tensorkomponenten, tensor components 14. Tensorpolynom, tensor polynomial 21. Tensorpotenzreihe, tensor power series 21, thermische Zwangsbedingungen, thermal

constraints 329. thermisches Gleichgewicht in einer einfachen

Substanz, thermal equilibrium in a simple material 298-301.

Thermodynamik der Diffusion, thermodynamics of diffusion 541. einfacher Substanzen, of simple materials 363-381, irreversibler Prozesse, of irreversible processes 373.

thermodynamischer ProzeB, thermodynamic process 295.

Thermoelastizitat, thermo-elasticity 355-363. - mit linearer Viskositat, with linear

viscosity 357. thermomechanisches Potential, thermo

mechanical potential 299. Thermostatik einfacher Substanzen, thermo

statics of simple materials 300. thermostatischer Grenzwertsatz, thermo

static limit theorem 371, Torsion, falsche Theorien, wrong theories 236. - eines Rohres, of a tube 191-193, 232 bis

237 --', Theorie zweiter Ordnung, second-order

theory 232-237. - eines Zylinders, of a cylinder 191-193,

343f.,352f. Torsionsstarrheit, torsional rigidity 266. Torsionsstromung, torsional flow 458-464. TOUPINS elektromechanische Theorien, electro-

mechanical theories of Toupin 385-389· TOUPINS orientierte hyperelastische Sub

stanzen, Toupin's oriented hyperelastic materials 391-397.

Transponierte eines Tensors, transpose of a tensor 15.

transversal isotrope Flussigkeiten von ERICKSEN, transversely isotropic fluids of Ericksen 527-528.

transversale Isotropie, transverse isotropy 82. Transversalwelle, transverse wave 268, 280. trikline Festkorper, triclinic solids 85.

Uberlagerte elastische Verzerrung (Sa tz), superimposed elastic strain (theorem) 250.

trberspannung, extra stress 71, trberstabilitat, superstability 255, 257. Umkehrbarkeit des Kraft-Dehnungs-Zu-

sammenhanges, IF 5 condition (invertibility of force-stretch) 156.

Undehnbarkeit, inextensibility 72. Ungleichung von COLEMAN und NOLL,

inequality of Coleman and Noll 319-324. Ungleichungen fUr elastische Substanzen,

inequalities for elastic materials 153-171, der Krafteordnungen, O-F inequalities (ordered forces) 157. fUr Kreisprozesse, for cyclical processes 369f.

unverzerrte Zustande eines isotropen Materials, undistorted states of an isotropic material 78, 82, 139, 151,

unverzerrter Zustand einer anisotropen Flussigkeit, undistorted state of a subfluid 87. -- eines Festkorpers, of a solid 85.

Variationsprinzipien fUr hyperelastische Substanzen, variational principles for hyperelastic materials 326-328.

Vektorkomponenten, vector components 14. Verbiegung, innere, buckling, interior 130. VerformungsstoB, strain impulse 107-108. Verruckungsgradient, displacement gradient

130. Verschiebungsoperator, shifter 49. Versetzung, dislocation 126. Versetzungen, Kontinuumstheorie, continuum

theory of dislocations 88-92. - in elastischen Korpern, dislocation in elas

tic bodies 125-126. Versetzungsdichte, dislocation density 92. V erzerrungs-Energie-Funktion, strain-energy

function 302, 307-316, 397f. -, keine experimentelle Prufung ihrer Exi

stenz, no experimental test of existence 344. virtuelle Arbeit, virtual work 306. Viskoelastizitat, klassische Theorie, visco

elasticity, classical theory 116. -, line are, linear 109, 378. Viskometrie, Theorien, viscometry, theories

465-468. viskometrische Funktionen, viscometric

functions 13, 436, 495, 504. - - fUr Poly-isobutylen, for poly-iso

butylene 467 f. viskometrische Stromung, viscometric flow

432, 435-440. -- der anisotropen Flussigkeiten von ERICKSEN, of Ericksen's anisotropic fluids 533-537·


viskometrische Strbmung, asymptotische Theorie, viscometric flow, asymptotic theory 488-490.

Viskositat, viscosity 65. -, klassische Theorie, classical theory 113 bis

117. -, natiirliche, natural 437. Viskositatsfunktion, viscosity function 436. vollkommene Elastizitat s. Hyperelastizitat,

perfect elasticity see hyperelasticity 304. vollkommene Fliissigkeit, perfect fluid 149. vollkommene Substanzen, Thermodynamik,

perfect materials, thermodynamics 296 bis 298.

Volumanderung in der Theorie zweiter Ordnung, volume change in second-order theory 240, 346.

Volumkraft, body force 40. Vorgang, dynamischer, dynamical process

41. Vorgeschichte einer Funktion, history of a

function 52.

Warme und Elektrizitat, Analogie, heat and electricity, analogy 388.

Warmeabsorption, heat absorption 294. WarmefluE, heat flux 294. Warmeleitung, heat conduction 294f., 384. Wangsche Theorien des schwindenden Ge-

dachtnisses, Wang's theories of fading memory 105, 112-113.

Wechsel des Bezugssystems, change of frame 41.

Weissenberg-Effekt, Weissenberg effect 453f. Weissenbergsche Aussage, Weissenberg's

assertion 484. Wellen s. auch Beschleunigungswellen, waves

see also acceleration waves . -, ebene infinitesimale, plane infinitesimal

273-278. endlicher Amplitude, of finite amplitude 283f. hbherer Ordnung, of higher-order 272f., 283.

--, homentrope und homotherme, homentropic and homothermal 272, 335, 383f. in inkompressiblen Substanzen, in incompressible materials 291-294. in isotropen Substanzen, in isotropic materials 278-291.

Wellenausbreitung, wave propagation 267 bis 294, 332-335.

- in Su bstanzen mit Gedachtnis, in materials with memory 382-385.

Wellengeschwindigkeit in zweiter Ordnung, second-order wave speed 288-291.

wirbelfreie Bewegung, irrotational motion 67, 75.

wirbelfreie homogene Vorgeschichte, irrotational homogeneous history 67.

Wirkungsprinzip von TOUPIN, action principle of Toupin 392.

Zahigkeit s. Viskositat. zeitabhangige Deformation von Rohren,

time-dependent deformations of tubes 212f. Zeitablauf, natiirlicher, time-lapse, natural

437. Zeitableitungen, materielle und raumliche,

time derivatives, material and spatial 39. Zenersche Formel fiir Volumanderung in

zweiter Naherung, Zener's formula for second-order change of volume 346.

zirkulationserhaltende Bewegung, circulation preserving motion 75.

zulassiger thermodynamischer ProzeE, ad-missible thermodynamic process 365.

zulassiger Vorgang, admissible process 44. Zustand, state 329. Zustandsgleichung, equation of state 133. -, kalorische, caloric 298, 361. Zwangsbedingungen, innere, constraints,

internal 69-73. -, thermische, thermal 329. Zylinder, koaxiale, Strbmung zwischen ihnen,

cylinders, coaxial, flow between them 446 bis 452.

- -, Radialschwingungen, radial oscillations 214-217·

-, Streckung durch Verdrehen, extension by twisting 193, 352.

-, verschiedene Deformationen, various deformations 189-195.

Zylinderkoordinaten, cyclindrial co-ordinates 19.

Zylindersektor, Geradebiegen und Dehnen, cylindrical sector, straightening and stretching 188f., 343.

zylindrisches Rohr, Streckung, Aufweitung und Scherung, cylindrical tube, extension, inflatlion and shear 353.

Subject Index. (English- German.)

Where English and German spelling of a word is identical the German version is omitted.

Absorption of waves, Absorption von Wellen 276.

Acceleration field, Beschleunigungsfeld 39. Acceleration gradients, Beschleunigungs

gradienten 54. Acceleration waves see also waves, Be

schleunigungswellen s. auch Wellen 267 to 272. -, growth and decay, Anwachsen und Zerfall 384. - in hypo-elastic materials, in hypoelastischen Substanzen 413 -415.

Acoustical axes, akustische Achsen 268, 414 . Acoustical tensor, akustischer Tensor 268. Acoustic tensor, symmetry, akustischer Ten-

sor, Symmetrie 384. Action principle of TOUPIN, Wirkungs

prinzip von Toupin 392. Adiabatic see isentropic, adiabatisch s. isen

trop. Adiabatic stability, adiabatische Stabilitiit

330. ADKINS' reciprocal theorem, Reziprozitatssatz

von Adkins 207. Admissible process, zuliissiger Vorgang 44. Admissible thermodynamic process, zuliissi-

ger thermodynamischer ProzefJ 365. Aeolotropic solid, anisotroper Festkorper 82. - -, stored energy, gespeicherte Energie 312. Aeolotropy, Anisotropie 197. -, curvilinear, krummlinige 91. AIRY's stress function, Airysche Spannungs

funktion 204. Amplitude of wave, Amplitude einer Welle

268, 283. Angular momentum (see moment of mo

mentum), Drehimpuls 40. Angular oscillations of second-grade fluids,

Drehschwingungen von Fliissigkeiten zweiten Grades 510.

Anholonomic components, anholonome Komponenten 1 5.

Anisotropic fluids of COLEMAN, anisotrope Fliissigkeiten von Coleman 88.

of ERICKSEN, von Ericksen 523-537. - of GREEN, von Green 521-523. - of WANG, von Wang 86-88, 151, 314-316, 473-475·

Anisotropy see also Aeolotropy. Apparent moduli and elasticities, scheinbare

M aduln und Elastizitiitskoeffizienten 239seq., 251 seq.

Astatic load, astatische Belastung 127. Axial oscillations of second-grade fluids,

A xialschwingungen von Fliissigkeiten zweiten Grades 509seq.

Axis of equilibrium, Gleichgewichtsachse 136, 258.

Basic representation theorem of CAUCHY, Darstellungshauptsatz von Cauchy 29.

Basic stability theorem, Fundamentalsatz der Stabilitiit 253.

Basis vectors, Basisvektoren 14seq., 23. B-E inequalities, Baker-Ericksensche Un

gleichzmgen 158-171,175,183,281,293. Bending, Biegung 186, 194, 211. - of a block, eines Blocks 186-188, 211,

342seq. BERNSTEIN'S theorem on waves, Bernstein

scher Wellensatz 332. BETTI'S theorem, Bettischer Satz 324seq. Block, bending and stretching, Block, Biegen

und Dehnen 186-188, 211, 342. Body, definition, Korper, Definition 37. -, homogeneous, homogener 59, 90. Body force, Volumkraft 40. BOLTZMANN'S theory of visco-elasticity,

Boltzmannsche Theorie der Viskoelastizitiit 116.

BORDONI'S special theory of elasticity, Bordanis spezielle Elastizitiitstheorie 348.

Boundary-value problems of elasticity, Randwertprobleme der Elastizitiitsthearie 125 to 129. - for hyperelastic materials, fiir hyperelastische Substanzen 326.

BRESSAN'S theorem on waves, Bressanscher Wellensatz 282.

BRILLOUIN'S coefficients of second-order elasticity, Brillouinsche elastische Koeffizienten zweiter Ordnung 230.

BRILLOUIN'S principle, Brillouinsches Prinzip 360.

Buckling, interior, inn ere Verbiegung 130.

Caloric equation of state, kalorische Zustandsgleichung 298, 361.

Capillarity theory of KORTEWEG, Kapillaritiitstheorie von Korteweg 513-515.

CAPRIOLI'S work theorem, Caprialischer Arbeitssatz 305.

CAUCHY'S basic representation theorem, DarsteUungshauptsatz van Cauchy 29.

592 Subject Index.

Cauchy-Green tensors, Cauchy-Greensche Tensoren 53.

CFT 2. Change of frame, Wechsel des Bezugssystems

41, Channel flow, Kanalstramung 443 seq. Christoffel symbols, Christoffelsche Symbole

19seq. C-inequalities (classical), klassische Unglei

chungen 153. Circular pipes, flow in them, kreiszylindrische

Rohrleitungen, Stramung darin 448-452. Circulation-preserving motion, zirkulations

erhaltende Bewegung 75. Clausius-Duhem inequality, Clausius-Du

hemsche Ungleichung 295, 361, 363seq. Climbing in steady Couette flow, Klettern in

stationiirer Couette-Stramung 452-455. C-N condition, Coleman-N ollsche Bedingung

157,321,333. C-N+ condition, Coleman-Nollsche CN+-Be

dingung 323. COLEMAN'S thermodynamics of simple ma

terials, Colemansche Thermodynamik einfacher Substanzen 363-381,

COLEMAN'S work theorem, Colemanscher A rbeitssatz 306.

COLEMAN and NOLL'S inequality, ColemanNollsche Ungleichung 319--324.

COLEMAN and NOLL'S stability theorem, Coleman-Nollscher Stabilitiitssatz 330.

COLEMAN and NOLL'S theory of fading memory, Coleman-N ollsche Theorie des schwindenden Gediichtnisses 101-117.

Compatibility condition, Kompatibilitiitsbedingung 127.

Compatibility conditions for principal waves, Kompatibilitiitsbedingungen fur Hauptwellen 286-288. - of TOUPIN and BERNSTEIN, von Toupin und Bernstein 277, 335.

Compatibility theorem of SIGNORINI, Kompatibilitiitssatz von Signorini 225.

Complementary strain-energy, komplementiire Deformationsenergie 327.

Compressible elastic bodies, all possible deformations, kompressible elastische Karper, Gesamtheit der maglichen Deformationen 171-179, 336seq. - -, homogeneous strain, homogene Verformung 171-179.

Conductors of heat, W iirmeleiter 384. Cone-and-plate flow, Stramung zwischen

Kegel und Platte 461-464. Configuration, definition, Konfiguration, De

finition 37. -, local, lokale 52. Connection, material, materielle Konnektion

89. Constant stretch history, konstante Streck

vorgeschichte 438-440. Constitutive equation of an elastic fluid,

M aterialgleichung einer elastischen Flussigkeit 149.

Constitutive equation of an elastic material, Materialgleichung einer elastischen Substanz 119. -, general mechanical, allgemeine mechanische 57 - 58. - of a hyperelastic material, einer hyperelastischen Substanz 302. - of an incompressible isotropic elastic material, einer inkompressiblen isotropen elastischen Substanz 148.

Constitutive equations, M aterialgleichungen 2,36,44. - of COLEMAN, von Coleman 364seq. - of differential-type materials, fur Substanzen vom Differentialtyp 93 seq. -, dimensionally reduced form, dimensionslose 65seq., 120. - of rate-type materials, fur Substanzen von geschwindigkeitsabhiingiger Struktur 95.

Constraints, internal, innere Zwangsbedingungen 69-73.

-, thermal, thermische 329. Contact force see also stress, Kontaktkraft

s. auch Spannung 40. Continuity equation, Kontinuitiitsgleichung

39. Continuum and molecular theories compared,

Kontinuumstheorien und molekulare Theorien, Vergleich 5.

Contravariant components, kontravariante Komponenten 14seq.

Contravariant derivatives, kontravariante A bleitungen 16.

Convected stress-rate, mitgefiihrte Spannungsgeschwindigkeit 96, 97.

Co-ordinates, material and spatial, Koordinaten, materielle und riiumliche 37, 39.

Co-ordinate systems, Koordinatensysteme 19seq.

Cosserat material, Cosseratsche Substanz 397. COSSERATS' theory of polar elastic materials,

Cosseratsche Theorie polarer elastischer Substanzen 389seq.

Couette flow, Couette-Stramung 449seq. COULOMB'S experiments on torsion, Coulomb

sche Experimente iiber Torsion 236. Couple density, Kriiftepaardichte 394. Couple-stress tensor, M omentenspannungs

tensor 396, 525. Covariant components, kovariante Kompo

nenten 14 seq. Covariant derivatives, kovariante Ableitungen

16. Crystal classes, Kristallklassen 83. Cyclic processes, general theorem, Kreis

prozesse, allgemeiner Satz 381. - -, inequalities, Ungleichungen 369seq. Cylinder, extension by twisting, Zylinder,

Streckung durch Verdrehen 193, 352. -, radial oscillations, Radialschwingungen

214-217. -, various deformations, verschiedene De

formationen 189-195.

Subject Index. 593

Cylinders, coaxial, flow between them, koaxiale Zylinder, Stromung zwischen ihnen 446-452.

Cylindrical co-ordinates, Z ylinderkoordinaten 19·

Cylindrical sector, straightening and stretching, Zylindersektor, Geradebiegen und Dehnen 188seq., 343.

Cylindrical tube, extension, inflation and shear, zylindrisches Rohr, Streckung, Aufweitung und Scherung 353.

DA SILVA'S theorem on torques, Da Silvascher Drehmomentensatz 128.

Definite conductor of heat, definiter W iirmeleiter 384.

Deformation function, relative, Deformationsfunktion, relative 49.

Deformation gradient, Deformationsgradient 49.

Deformation, local, 10k ale Deformation 52. Deformations possible in all compressible

elastic bodies, Deformationen, die moglich sind in allen kompressiblen elastischen Korpern 171-179, 336seq. possible in all incompressible elastic bodies, die moglich sind in allen inkompressiblen elastischen Korpern 337-342.

Density of mass, Dichte der Masse 38. Determinant of a tensor, Determinante eines

Tensors 15, 23 seq. - -, its gradient, ihr Gradient 25. Determinism, Determinismus 12, 36, 56. Differential equations of motion for super-

imposed infinitesimal displacement, Bewegungsgleichungen filr ilberlagerte infinitesimale Verrilckungen 247.

Diffusion, framework of theories, Dillusion, Rahmentheorie 537-541.

Dilatation group, Dilatationsgruppe 86. Dilatation of hypo-elastic material, Dilata

tion einer hypoelastischen Substanz 416. -, uniform, gleichformige 173. Dimensional invariance, Dimensionsinvarianz

64-65. Directors of an oriented medium, Direktoren

eines orientierten Mediums 389, 392. Dislocation, Versetzung 126. Dislocation density, Versetzungsdichte 92. Dislocations, continuous, in elastic bodies,

K ontinuierliche Versetzungen in einem elastischen Korper 125-126.

Dislocations, continuum theory of, Kontinuumstheorie der Versetzungen 88-92.

Dispersion of waves, Dispersion von Wellen 276.

Displacement gradient, Verrilckungsgradient 130.

Dissipation principle, Dissipationsprinzip 295.

DUHEM's identity for acoustical tensors, Duhemsche I dentitiit filr akustische T ensoren 335.

DUHEM'S theorem on waves, Duhemscher Satz ilber Wellen 272. Handbuch der Physik, Bd. UI/3.

DUHEM's theorem on wave speeds, Duhemscher Satz ilber Wellengeschwindigkeiten 335.

Dyadic product of two vectors, dyadisches Produkt zweier Vektoren 15.

E-inequalities, E-Ungleichungen 171. Elastic body, elastischer Korper 125. Elastic dielectric, elastisches Dielektrikum 385

to 388. Elastic fluid, elastische Flilssigkeit 148, 480. - -, stored energy,gespeicherte Energie 313. Elastic material, elastische Substanz 106, 117.

- as approximation, als Niiherung 111. -, its definition, Definition 13, 117, 119 seq. -, isotropy group, Isotropiegruppe 122. -, polar, polare 389-401. -, reinforced, verstiirkte 122.

Elastic solid, elastischer F estkorper 149, 170. Elastic stability, elastische Stabilitiit 252-260. Elastic su bfluid, elastische anisotrope Flilssig-

keit 151, Elastic theories of fluids, elastische Theorien

der Flilssigkeiten 480 seq. Elasticities, apparent, Elastizitiitskoellizien

ten, scheinbare 239seq., 251 seq. - of an elastic material, einer elastischen

Substanz 132. -, number of independent ones, A nzahl un

abhiingiger 309seq. Elasticity, classical infinitesimal theory, Ela

stizitiit, klassische infinitesimale Theorie 117. of n-th order, n-ter Ordnung 228.

-, reduced constitutive equations, reduzierte Materialgleichungen 113, 120seq.

Elastostatics, differential equation, Elastostatik, Dillerentialgleichung 127.

- of simple materials, einfacher Substanzen 123.

Electricity and heat, analogy, Elektrizitiit und Wiirme, Analogie 388.

Electromechanical theories, elektromechanische Theorien 385-389.

Ellipsoid of polarization, Polarisationsellipsoid 332.

Elliptical tube, secondary flow, elliptisches Rohr, sekundiire Stromung 503.

Energy balance, Energiebilanz 294seq. Energy functional, Energiefunktional 298. Entropy, Entropie 133, 294 seq. Entropy function, Entropiefunktion 301. Entropy inequality, Entropieungleichung 295,

357. Entropy relation, Entropiebeziehung 302, 368. Equation of continuity, Kontinuitiitsgleichung

39· Equation of state, Zustandsgleichung 133. - -, caloric, kalorische 298, 361, Equipresence principle, Jiquipriisenzprinzip

359seq., 364. Equivalence of motions and processes, Jiqui

valenz von Bewegungen und Vorgiingen 42, 43-45.

38a

594 Subject Index.

Equivalence theorem of COSSERAT-TouPIN, }fquivalenzsatz von Cosserat und Toupin 395. - for higher-order waves, fur Wellen hoherer Ordnung 273.

ERICKSEN'S analysis of deformations possible in all compressible elastic bodies, Ericksens Untersuchung der moglichen De/ormationen in allen kompressiblen elastischen J{orpern 336seq. - - - in all incompressible elastic bodies, in allen inkompressiblen elastischen J{orpern 337-342.

ERICKSEN'S anisotropic fluids, Ericksensche anisotrope Flussigkeiten 523-537.

ERICKSEN'S work theorem, Ericksenscher A rbeitssatz 307.

E-T inequalities (extension-tension), Dehnungs-Spannungs- Ungleichungen 157.

Euclid invariance, Euklidische Invarianz 392, 395·

Euclidean action, Euklidische Wi,·kung 389, 392.

event (= point in space-time), Ereignis (= Weltpunkt) 41.

Existence and uniqueness theorems in elasticity, Existenz- und Eindeutigkeitssiitze der Elastizitiitstheorie 133-139.

Extension of a cylinder by twisting, Streckung eines Zylinders durch Verdrehen 193, 352.

- of hypo-elastic material, einer hypoelastischen Substanz 417 seq.

-, steady, mit konstanter Geschwindigkeit 472seq.

- and torsion interrelated, und Torsion, gegenseitige Beziehung 264seq.

Extra stress, Uberspannung 71.

Fading memory, schwindendes Gediichtnis 36, 101-106, 112seq., 365.

Finite elasticity, differential equation of motion, endliche elastische De/ormation, Bewegungsgleichung 125.

First-order fluids, Flussigkeiten erster Ordnung 100.

Flow of anisotropic solids, Fliepbewegung anisotroper Festkorper 520-523.

Flow between coaxial cylinders, Stromung zwischen koaxialen Z ylindern 446-452. between rotating parallel plates, zwischen rotierenden parallelen Platten 458-464. of subfluids, von anisotropen FlUssigkeiten 473-475.

Fluidity, Fluiditiit 13. Fluids of different grades, FlUssigkeiten ver

schiedenen Grades 494. of different orders, verschiedener Ordnung 491. of first order, erster Ordnung 100. of second grade, zweiten Grades 504-513. of second order, zweiter Ordnung 100.

-, simple, ein/ache 427-513. -, special theories, spezielle Theorien 475 to

513.

Fluids of rate type, Flussigkeiten von geschwindigkeitsabhiingiger Struktur 482-484.

Forces and stresses, J{rii/te und Spannungen 39-41.

Frame, change of, Bezugssystem, Wechsel41. Frame-indifference, material, Bezugsindif

ferenz, materielle 12, 36, 44seq., 296. Frame-indifferent quantity, bezugsinditferen

te Grope 42. Fnlchet differential, Frechetsches Dif/erential

104. Free energy, freie Energie 301. - - minimum, Minimum 370. Free shape, freie Oberfliichenform 130. FRESNEL'S ellipsoid, Fresnelscher Ellipsoid

332. Fresnel-Hadamard theorem on wave propa

gation, Fresnel-Hadamardscher Satz uber Wellenausbreitung 168.

Fresnel quadric, Fresnelsche quadratische Form 268.

Fundamental theorem of HADAMARD on waves, Fundamentalsatz von Hadamard uber Wellen 271, 332seq. - on hyperelastic solids, uber hyperelastische F estkorper 311. - of NOLL on simple fluids, von Noll uber einfache Flussigkeiten 81. - on simple materials, uber einfache Substanzen 66.

GCN condition (generalized Coleman-Noll condition), GCN-Bedingung 162-169, 321.

GCNu condition, GCNu-Bedingung 160. GCNo- condition, GCNt-Bedingung 162. GCN+ condition, GCN+-Bedingung 166, 249,

257, 271, 281. Gibbs relations, Gibbssche Beziehungen 372,

381. GIBBS, COLEMAN and NOLL'S stability theo

rem, Gibbs-Coleman-N ollscher Stabilitiitssatz 331.

Grade of a fluid, Grad einer Flussigkeit 494, 504.

- of a material of differential type, einer Substanz vom DitferentiaUyp 111.

Gradient of a tensor function, Gradient einer Tensorfunktion 24-27.

- of a vector field, eines Vektorfeldes 15. Gradients of invariants, representations,

Gradienten von Invarianten, Darstellungen 34. of principal invariants, der Hauptinvarianten 25seq.

GREEN'S anisotropic fluids, Greensche anisotrope Flussigkeiten 521-523.

GREEN and RIVLIN'S multipolar elasticity, Green-Rivlinsche multipolare Elastizitiit 400seq.

Green-St. Venant strain tensor, Green-St. Venantscher Deformationstensor 221.

Grioli-Toupin material, Grioli-Toupinsche Substanz 400.

Gyration vector, Gyrationsvektor 386.

Subject Index. 595

HADAMARD'S fundamental theorem on waves, Hadamardscher Fundamentalsatz iiber Wellen 271, 332seq.

HADAMARD'S inequality, Hadamardsche Ungleichung 253, 257.

Hagen-Poiseuille efflux formula, HagenPoiseuiUesche A usfluf3formel 466.

Hamilton-Cayley theorem, Hamilton-Cayley-scher Satz 26.

Heat absorption, W lirmeabsorption 294. Heat conduction, Wlirmeleitung 294 seq. Heat and electricity, analogy, Wlirme und

Elektrizitlit, A nalogie 388. Heat flux, W lirmefluf3 294. Helical flow, schraubenfiirmige Striimung 445

to 452. Hemitropic tensorfunction, hemitrope Tensor

funktion 24. Hemitropy, Hemitropie 358. History of finite hyperelasticity, Geschichte

der H yperelastizitlit endlicher Deformationen 304.

- of a function, Vorgeschichte einer Funktion 52.

Higher-order elasticities, experimental, Elastizitlitskoeffizienten hiiherer Ordnung, Experimentelles 230.

Higher-order waves, Wellen hiiherer Ordnung 272seq., 283.

Holohedry see isotropy. Homentropic waves, homentrope Wellen 272,

335,383seq. Homogeneity of material lost by strain, Ho

mogenitlit der Substanz, Verlust bei Verzerrung 251.

Homogeneous body, homogener Kiirper 59, 90. Homogeneous flow of ERICKSEN'S anisotropic

fluids, homogene Striimung der anisotropen Fliissigkeiten von Ericksen 530 to 533.

Homogeneous motions, isochoric, homogene Bewegungen, isochore 74.

Homogeneous pure-stretch history, homogene reine Dehnungs- Vorgeschichte 66.

Homogeneous strain, homogene Verzerrung 171-183.

Homogeneous strain history, homogene Verzerrungs- V orgeschichte 62.

Homothermal waves, homotherme Wellen 272, 335, 383seq.

Hydrostatic pressure, effect on wave speed, hydrostatischer Druck, Einfluf3 aUf Wellengeschwindigkeit 284seq.

Hydrostatic tension states in elastic materials, hydrostatische SPannungszustlinde in elastischen Substanzen 170.

Hyperelastic material, hyperelastische Substanz 117, 294seq.

- -, definition, Definition 302. Hyperelastic materials of second grade, hyper

elastische Substanzen zweiten Grades 397 to 400. -, special properties of solutions, spezielle Eigenschaften der Liisungen 342 to 344. Handbuch der Physik, Bd. III/3.

Hyperelastic solids, fundamental theorem. hyperelastische Festkiirper. Fundamentalsatz 311.

Hyperelastic stability, hyperelastische Stabilitlit 328-332.

Hyperelastic subfluids, hyperelastische anisotrope Fliissigkeiten 314-316.

Hyperelasticity. definition, Hyperelastizitlit, Definition 13.

Hyperstress tensor, Hyperspannungstensor 395, 398.

Hypo-elastic material, definition, hypoelastische Substanz, Definition 401 seq.

Hypo-elastic response functions, hypoelastische A uswirkungsfunktionen 404.

Hypo-elastic waves, hypoelastische Wellen 413-415.

Hypo-elastic yield, hypoelastisches Flief3en 420-426.

Hypo-elasticity, Hypoelastizitlit 13, 117, 401 to 426.

-, relation to elasticity, Beziehung zur Elastizitlit 406-411.

Ideal material, ideale Substanz 2, 44. IFS condition (invertibility of force-stretch),

Umkehrbarkeit des Kraft-Dehnungs-Zusammenhanges 1 56.

Incompressibility, Inkompressibilitlit 71. Incompressible see also isochoric. Incompressible elastic bodies, all possible de-

formations, inkompressible elastische Kiirper, Gesamtheit der miiglichen Deformationen 337-342.

Incompressible elastic material, inkompressible elastische Substanz 121.

- - -, homogeneous strain, homogene Verformung 1 79-183.

Incompressible isotropic elastic material, inkompressible isotrope elastische Substanz 147seq.

Incompressible isotropic material, secondorder elasticity, inkompressible isotrope Substanz, Elastizitlit zweiter Ordnung 241 to 246.

Incompressible material, wave propagation, inkompressible Substanz, Wellenausbreitung 291-294.

Inequalities for cyclical processes, Ungleichungen fiir Kreisprozesse 369seq.

- for elastic materials, fiir elastische Substanzen 153-171.

Inequality of COLEMAN and NOLL, Uugleichung von Coleman und Noll 319--324·

Inextensibility, Undehnbarkeit 72. Infinitesimal plane waves, infinitesimale

ebene Wellen 273-278. Infinitesimal rotation tensor, infinitesimaler

Verdrehungstensor 11 5. Infinitesimal stability, infinitesimale Stabili

tlit 252-260. Infinitesimal strain superimposed upon a

given strain, infinitesimale Verzerrung, die einer gegebenen Verzerrung iiberlagert ist 250, 325.

38b

596 Subject Index.

Infinitesimal strain tensor, infinitesimaler Verzerrungstensor 115.

Infinitesimal theory of elasticity, infinitesimale Elastizitatstheorie 11 7.

Infinitesimal visco-elasticity, infinitesimale Viskoelastizitat 116.

Inflation of a tube, Aufweitung eines Rohres 189-195, 211 seq., 343seq., 353.

Internal constraints, innere Zwangsbedin-gungen 69-73.

Internal energy, innere Energie 294. Invariants, lists, I nvarianten, Listen 30 seq. -, multilinear, multilineare 30. -, polynomial, polynomiale 28-30. -, representation, Darstelll~ng 27-32. - of a tensor, eines Tensors 22seq. Irreversible thermodynamics, irreversible

Thermodynamik 373. Irrotational homogeneous history, wirbel

freie homogene V orgeschichte 67. Irrotational motion, wirbelfreie Bewegung 67,

75· Isentropic elasticity, isentrope Elastizitat

133. Isochoric see also incompressible. Isochoric homogeneous motions, isochore

homogene Bewegungen 74. Isochoric motion, isochore Bewegung 39, 55. Isothermal cyclic processes, isotherme Kreis

prozesse 372. Isothermal elasticity, isotherme Elastizitat

133. Isothermal stability, isotherme Stabilitat 330. Isotropic elastic material, isotrope elastische

Substanz 139. - - -, response coefficients, elastische

K oeffizienten 140 seq. Isotropic hyperelastic material, isotrope

hyperelastische Substanz 313seq., 317 to 319.

Isotropic incompressible elastic material, isotrope inkompressible elastische Substanz 147seq.

Isotropic material of differential type, isotrope Substanz vom Differentialtyp 94.

- -, wave propagation, Wellenausbreitung 278-291.

Isotropic materials, isotrope Substanzen 78seq. Isotropic tensor function, isotrope Tensor-

funktion 22-24, 34. - - -, representation, Darstellung 32, 34. Isotropy, definition, I sotropie, Definition 358. Isotropy group, Isotropiegruppe 76-79.

- of an elastic material, einer elastischen Substanz 122. - of hyperelastic subfluids, hyperelastischer anisotroper FlUssigkeiten 314 to 316.

Isotropy groups of hyperelastic materials, I sotropiegruppen hyperelastischer Substanzen 310-313.

JOHN'S special theory of elasticity, Johns spezielle Elastizitatstheorie 349.

Jump continuation, Sprungfortsetzung 374.

Kelvin effects, Kelvinsche Effekte 176, 236, 345.

Kinetic stability, kinetische Stabilitat 259. KIRCHHOFF'S special theory of elasticity,

K irchhoffs spezielle Elastizitatstheorie 348. KORTEWEG'S theory of capillarity, Korteweg

sche Theorie der Kapillaritat 513-515.

Lame coefficients of elasticity, Lamesche Elastizitatskoeffizienten 116-117.

- - of viscosity, Lamesche Viskositatskoeffizienten 113.

Lineal flow, geradlinige Stromung 429-432, 441-445.

- - of second-grade fluids, von Fliissigkeiten zweiten Grades 510-513.

Lineal oscillation flow, geradlinige Oszillationsstromung 444seq.

Linear tensor function, lineare Tensorfunktion 22, 33.

Linearly viscous material, linear viskoseSubstanz 114.

Liquid crystals (subfluids, anisotropic fluids), fliissige Kristalle 86-88, 151, 314-316, 473-475,523-537·

Local action, principle, lokale Wirkung, Prinzip 12, 36, 56.

Local configuration, lokale Konfiguration 52. Local deformation, lokale Deformation 52. Localization of a motion, Lokalisierung einer

Bewegung 51 seq. Locally visco metric motion, lokal viskometri

sche Bewegung 432. Longitudinal wave, Longitudinalwelle 268,280.

Macromedium, Makromedium 391. Macroquantities in polar elastic materials,

M akrogrof3en in polaren elastischen Substanzen 392.

Magnitude of a tensor, Betrag eines Tensors 15.

Mass density, Massendichte 38. Mass distribution, Massenverteilung 38. Material connection, Stoffkonnektion 89. Material co-ordinates and description, materi-

elle Koordinaten und Beschreibung 37, 39. Material frame-indifference (principle), Prin

zip der Bezugsindifferenz 36, 44, 296. Material functionals, Substanzfunktionale 431 . Material of grade n (see also grade), Substanz

vom Grad n (s. auch Grad) 63. Material isomorphism, Stoffisomorphie 59. Material time derivative, materielle Zeit

ableitung 39. Material uniformity of a body, Stoffgleichheit

eines Korpers 59, 90. Materially uniform elastic body, stoffgleicher

elastischer Korper 126. Materials of differential type, Substanzen vom

Differentialtyp 93-95, 111. of integral type, vom I ntegraltyp 98-101. of mixed integral-differential type, gemischten Integral-Differentialtyps Wi. of rate type, von geschwindigkeitsabhangiger Struktur 95-98.

Subject Index. 597

Maximum entropy, theorem on, Satz vom Maximum der Entropie 380.

Maxwellian fluid, TRUESDELL'S theory, Maxwellsche Fliissigkeit, Truesdellsche Theorie 515-520.

Memory see fading memory. Micromedium, Mikromedium 391. Microquantities in polar elastic materials,

Mikrograf3en in polaren elastischen Substanzen 392, 395.

Minimum free energy, theorem on, Satz vom Minimum der freien Energie, 370.

Minimum internal energy, theorem on, Satz vom Minimum der inneren Energie, 380.

Mixture of interdiffusing materials, Gemisch ineinander diffundierender Substanzen 537-541.

Moduli, apparent, Moduln, scheinbare 239seq. Molecular and continuum theories compared,

M olekulartheorien und Kontinuumstheorien, Vergleich 5.

Moment condition, M omentenbedingung 258.

Moment of momentum, Drehimpuls 40. Moments of a tensor, Momente eines Tensors

23. - -, their gradients, ihre Gradienten 27. Momentum, I mpuls 40. Monotone transformation, monotone Trans

formation 161. Mooney-Rivlin theory of rubber, Mooney

Rivlinsche Theorie des Gummis 349 to 354.

Motion of a body, general description, Bewegung eines Karpers, allgemeine Beschreibung 38.

Multilinear invariants, multilineare I nvarianten 30.

Multilinear tensor function, Tensorfunktion, multilineare 22, 34seq.

Multipolar elasticity, multipolare Elastizitiit 400seq.

MURNAGHAN'S coefficients of second-order elasticity, Murnaghansche elastische Koeffizienten zweiter Ordnung 230.

Natural state, naturlicher Zustand 306, 311, 322.

Natural units of elasticity, time-lapse etc., naturliche Einheiten von Elastizitiit, Zeitablauf usw. 64.

Navier-Stokes equations, N avier-Stokessche Gleichungen 476.

Navier-Stokes theory of viscometry, NavierStokessche Theorie der Viskometrie 113 seq. 467.

Neo-Hookean theory of elasticity, neo-Hookesche Theorie der Elastizitiit 350.

NOLL'S theorem on flows with constant stretch history, N ollscher Satz uber Stramungen mit konstanter Streckvorgeschichte 438. - on simple fluids, Fundamentalsatz uber einfache Fliissigkeiten 81.

NOLL'S theorem on simple materials, Fundamentalsatz uber einfache Substanzen 66.

Non-conductor of heat, Nichtleiter fur W iirme 384.

Normal stress in cone-and-plate flow, Normalspannung in der Stramung zwischen Kegel und Platte 463. end effects, Endeffekte 452-458.

Normal-stress difference in Couette flow, Normalspannungsdifferenz in der CouetteStramung 449. - in flow between coaxial cylinders, in Stramung zwischen koaxialen Z ylindern 448. - in flow between sliding cylinders, in Stramung zwischen gleitendenZylindern 451. - in a second-order fluid, in einer Flussigkeit zweiter Ordnung 493.

Normal-stress function, Normalspannungsfunktion 436.

- -, modified, modifizierte 446. Normal stresses in simple shear, Normal

spannungen bei einfacher Scherung 175 to 178.

Notations, Bezeichnungen 13-16.

Objective quantity see frame-indifferent quantity 42.

Objectivity see frame-indifference. Obliviator (influence function), Obliviator

(Einfluf3funktion) 102. O-F inequalities (ordered forces), Un

gleichungen der Kriifteordnungen 157. One-dimensional problems, eindimensionale

Probleme 10. Order of elasticity, Ordnung der Elastizitiit

228. of a fluid, einer Flussigkeit 491. of a material of integral type, einer Substanz vom Integraltyp 99. of a simple material, einer einfachen Substanz 109.

Oriented media, orientierte Medien 389. Orthogonal tensor, orthogonaler Tensor 15. Oscillations of second-grade fluids, Schwin-

gungen von Flussigkeiten zweiten Grades 509seq.

Partial gradient of a function of tensors, partieller Gradient einer Funktion von Tensoren 25.

Particles, definition, Teilchen, Definition 37· P-C inequality (pressure-compression),

Druck-Kompressions- Ungleichung 155. Perfect elasticity see hyperelasticity, voll

kommene Elastizitiit s. Hyperelastizitiit 304.

Perfect fluid, vollkommene Fliissigkeit 149. Perfect materials, thermodynamics, voll

kommene Substanzen, Thermodynamik 296-298.

Physical components, physikalische Komponenten 15.

598 Subject Index.

Piezo-caloric effect, its non-existence, piezokalorischer Effekt, seine N ichtexistenz 356.

Piola-Kirchhoff stress tensors, Piola-Kirchhoffsche Spannungstensoren 120, 124seq., 144, 169, 300, 320.

Pipe see also tube. Pipes, flow inside, Rohrleitungen, Stromung

darin 448-452. Plane infinitesimal waves, ebene infinitesimale

Wellen 273-278. Plane problems in elasticity, ebene Probleme

der Elastizitiitstheorie 204-208. - - in second-order elasticity, der Elasti

zitiitstheorie zweiter Ordnung 246. Plasticity, Plastizitiit 8, 420. Polynomial invariants, polynomiale In

varianten 28-30. Potential, thermomechanical, Potential, ther

momechanisches 299. Poynting effect, Poynting-Etfekt 177, 235,

345. POYNTING'S experiments on torsion, Poyn

tingsche Experimente uber Torsion 237. POYNTING'S problem, Poyntingsches Problem

193,352. Poiseuille flow, Poiseuille-Stromung 451 seq.

- of ERICKSEN'S anisotropic fluids, der anisotropen Flussigkeiten von Ericksen 536.

Polar decomposition theorem, polarer Zerlegungssatz 52.

Polar elastic materials, polare elastische Substanzen 389-401.

Polarization, electrical, Polarisation, elektrische 385.

Power series of tensors, Potenzreihe von Tensoren 21.

Pressure, Druck 149. -, effect on wave speed, EinflufJ aUf Wellen

geschwindigkeit 284seq. Principal forces, H auptkriifte 144, 317. Principal invariants of a tensor, Haupt

invarianten eines Tensors 23, 25. Principal stresses, Hauptspannungen 143. Principal stretchings, Hauptdehnungs

geschwindigkeiten 472. Principal waves, Hauptwellen 279.

-, compatibility conditions, Kompatibilitiitsbedingungen 286-288. -, fundamental theorems, Fundamentalsiitze 280 seq.

Principle of determinism for constrained materials, Prinzip der Determiniertheit fur Substanzen mit Z wangsbedingungen 70. - for stress, fur Spannungen 56.

Principle of equipresence, Prinzip der Aquipriisenz 359seq., 364. of fading memory, des schwindenden Gediichtnisses 36, 101, 103seq. of loca action, der lokalen Wirkung 12, 36, 56. of material frame-indifference, der materiellen Bezugsindifferenz 44, 296. - -, its history, seine Geschichte 45-47.

Principles of mechanical behavior, Prinzipien fur das mechanische Verhalten 36.

Process, dynamical, dynamischer Vorgang 41.

Product of tensors, Produkt von Tensoren 15.

Production of entropy, Entropieerzeugung 295.

Propagation condition, A usbreitungsbedingung 268.

Propagation speed, A usbreitungsgeschwindigkeit 268. --, second-order effects, Effekte zweiter Ordnung 288-291.

Quadric of polarization, quadratische Form der Polarisation 268.

Quasi-equilibrated motions of incompressible bodies, Quasigleichgewichts-Bewegungen inkompressibler Korper 208-214.

Radial oscillations of cylinders and spheres, Radialschwingungen von Zylindern und Kugeln 214-219, 354.

Reciprocal theorem of ADKINS, Reziprozitiitssatz von Adkins 207.

- - of BETTI, von Betti 324seq. Recollection of a history, Erinnerung an die

Vorgeschichte 102. Reduced constitutive equations, reduzierte

Materialgleichungen 66-69, 113, 120. Reference configuration, Bezugskonfigura

tion 48. REINER, basic contributions of, Reiners grund

legende Beitriige 9. Reiner-Rivlin fluids, Reiner-Rivlinsche Flus

sigkeiten 477-480, 486. REISSNER'S variational principle, Reissner

sches Variationsprinzip 328. Relative Cauchy-Green tensor, relativer

Cauchy-Greenscher Tensor 53. Relative deformation function, relative De

formationsfunktion 49. Relative deformation gradient, relativer De

formationsgradient 49. Relative rotation tensor, relativer Drehungs

tensor 53. Relative stretch tensor, relativer Streckungs

tensor 53. Representation of the gradient of an in

variant, Darstellung des Gradienten einer Invariante 34. of a vector-valued function, einer Funktion, die selbst ein Vektor ist 35.

Representation theorem, basic, of CAUCHY, Darstellungshauptsatz von Cauchy 29.

Representation theorem for isotropic tensor functions, Darstellungssatz fur isotrope Tensorfunktionen 32. - for linear isotropic tensor functions, fur lineare isotrope Tensorfunktionen 33. - for tensor invariants, fur Tensorinvarianten 28.

Subject Index. 599

Response function. Auswirkungsfunktion 296. - of an elastic material. einer elastischen Substanz 119. -. hypo-elastic. hypoelastische 404.

Response functional. A uswirkungsfunktional 36. 58. 61-

Retardation formulae of COLEMAN and NOLL. Retardierungs/ormeln von Coleman und Noll 110-111-

Retardation of a history. Retardierung einer Vorgeschichte 109.

Rheogoniometer of WEISSENBERG. Rheo-goniometer von Weissenberg 464.

Rheology. Rheologie 8. Rigidity. Starrheit 72. RIVLIN. basic contributions of. Rivlins grund

legende Beitriige 9. Rivlin-Ericksen fluids. Rivlin-Ericksensche

Flussigkeiten 481 seq. Rivlin-Ericksen tensors. Rivlin-Ericksensche

Tensoren 54. - -. generalization. Verallgemeinerung 516. RIVLIN and TOPAKOGLU'S interpretation of

SIGNORINI'S expansion. Rivlin-Topakoglusche Deutung der Signorinischen Entwick lung 227-229.

RIVLIN'S formula for the torsional modulus under extension. Rivlinsche Formel fur den Torsionsmodul bei Dehnung 192seq.

RIVLIN'S solutions in elasticity. Rivlinsche Losungen der Elastizitiitstheorie 171-197.

Rotating cylinders. flow between them. rotierende Zylinder. Stromung dazwischen 449seq.

rotation tensor. Drehungstensor 52. Rubber. experimental results. Gummi. ex

perimentelle Ergebnisse 171. 181 seq. -. theory of MOONEY and RIVLIN. Theorie

von Mooney und Rivlin 349-354.

S-E condition (strong ellipticity). S-E-Bedingung (starke Elliptizitiit) 129.132.147. 168seq .• 248. 254. 271. 281. 333.

Secondary flow. sekundiire Stromung 463 seq. - - in tubes. in Rohren 497-504. Second-grade fluids. Flussigkeiten zweiten

Grades 504--513. Second-grade hyperelastic materials. hyper

elastische Substanzen zweiten Grades 397 to 400.

Second-order effects in elasticity. elastische E//ekte zweiter Ordnung 229--246. - in isotropic hyperelastic materials. in isotropen hyperelastischen Substanzen 344-346.

Second-order elasticities. determination by wave speeds. elastische Konstanten zweiter Ordnung. Bestimmung aus Wellengeschwindigkeiten 290seq.

Second-order fluids. FlUssigkeiten zweiter Ordnung 100.

Second-order wave speed. Wellengeschwindigkeit in zweiter Ordnung 288-291-

Shear modulus. generalized. Scherungsmodul. verallgemeinerter 1 74. 182.

Shear-stress function. Scherspannungsfunktion 436.

Shearing. Schergeschwindigkeit 436. Shearing function. Schergeschwindigkeits

/unktion 436. Shearing of hypo-elastic material. Scherbe

wegung einer hypoelastischen Substanz 418-426.

-. rectilinear. geradlinige 76. Shifter. Verschiebungsoperator 49. Shock wave. Stof3welle 267. SIGNORINI'S expansion. Signorinische Ent

wicklung 219-227. SIGNORINI'S special theory of elasticity.

Signorinis spezielle Elastizitiitstheorie 348. Simple extension. einfache Dehnung 173.

180. Simple fluids. ein/ache Flussigkeiten 13. 78.

79--81. 427-513. Simple material. einfache Substanz 36.

60-63.78. - of order n. der Ordnung n 109. -. thermal equilibrium. thermisches Gleichgewicht 298-301.

Simple materials. basic properties. ein/ache Substanzen. Grundeigenschaften 66-69.

Simple shear of elastic bodies. ein/ache Scherung elastsicher Korper 174.

Simple shearing. einfache Scherbewegung 442seq.

- - of second-grade fluids. in Flussigkeiten zweiten Grades 506.

Simple solids. einfache Festkorper 78. 81 to 86.

Simultaneous invariant of several tensors (see also invariant). Invariante mehrerer Tensoren (s. auch Invarianten) 22. 24. 25. 31-

Small elastic deformations superimposed on large ones. kleine elastische Deformationen. die grof3en uberlagert sind 116-117.

Space-time. Raum-Zeit-Kontinuum 41. Spatial co-ordinates and description. riium

liche Koordinaten und Beschreibung 37. 39.

Spatial gradient. riiumlicher Gradient 39. Spatial time derivative. riiumliche Zeit

ableitung 39. Special theories of elasticity. spezielle Theo

rien der Elastizitiit 347-354. Speed of wave propagation. Geschwindigkeit

der Wellenausbreitung 268. - - -. second-order effects. Effekte zweiter

Ordnung 288-291-Spencer-Rivlin theorem on tensor invariants.

Spencer-Rivlinscher Satz uber Tensorinvarianten 31-

Spheres. radial oscillations. Kugeln. Radialschwingungen 217-219.

Spherical co-ordinates. Kugelkoordinaten 20.

Spherical shell. inflation and eversion. Kugelschale. Au/blasen und Umklappen 195. 344.

Spin tensor. Drehgeschwindigkeitstensor 54.

600 Subject Index.

Solutions in finite elasticity, approximate, Losungen der Elastizitiitstheorie endlicher Deformationen, geniiherte 219-267, 347 to 354. -, exact, exakte 171-219.

Stability, Stabilitiit 153. -, elastic, elastische 252-260. - of hyperelastic bodies, hyperelastischer

Karper 328-332. -, kinetic, kinetische 259. Stability theorem of HADAMARD, Stabilitiits

satz von Hadamard 253. State, Zustand 329. Static continuation, statische Fortsetzung 106,

369,371. Static stability, statische Stabilitiit 328. Statics of ERICKSEN'S anisotropic fluids,

Statik dey anisotropen Fliissigkeiten von Ericksen 528-530.

Steady extension, Dehnung, gleichmiifJig fortschreitende 76.

STOKES' principle of viscosity, Stokessches V iskositiitsprinzip 475 seq.

Stokesian fluid, TRUESDELL'S theory, Stokessche Fliissigkeit, Truesdellsche Theorie 485-488.

STOPPELLI'S theorem, Stoppellischer Satz 138.

Stored energy, Speicherenergie 302, 312. Stored-energy function, Speicherenergie

Funktion 302, 312seq., 315. - -, convex, konvexe 322. Straightening of a cylindrical sector, Gerade

biegen eines Zylindersektors 188seq., 343. Strain-energy function, Verzerrungs-Energie

Funktion 302, 307-316, 397seq. -, no experimental test of existence, keine experimentelle Priifung ihrer Existenz 344.

Strain impulse, VerformungsstofJ 107-108. Stress, Spannung 39seq. Stress-entropy relation, Spannungs-Entropie

Beziehung 367seq. Stress-entropy tensor, Spannungsentropie

Tensor 365. Stress, principal axes, 5pannungshaupt

achsen 142. Stress principle, Spannungsprinzip 40. Stress relation, Spannungsbeziehung 297, 300

to 302, 313, 368. - -, inversion, Umkehrung 327. Stress relaxation, Spannungsrelaxation 47,

106seq., 369. Stress-relaxation function, Spannungsrela

xationsfunktion 115. - -, COLEMAN'S theorem, Coleman scher

5atz 378. Stress-strain relation, Spannungs- Verfor

mungs-Beziehung 119. Stress tensor, convected, SPannungstensor,

mitgefiihrter 67. - -, non symmetrical, unsymmetrischer 389. Stress vector, 5pannungsvektor 40. Stretch history, constant, konstante Streckvor

geschichte 438-440.

Stretch tensors, right and left, Strecktensoren, rechter und linker 53.

Stretching tensor, 5treckgeschwindigkeitstensor 54.

Structural and continuum theories compared, Strukturtheorien und Kontinuumstheorien, Vergleich 5.

ST. VENANT'S special theory of elasticity, St. Venants spezielle Elastizitiitstheorie 348.

Subfluids (liquid crystals), anisotrope Fliissigkeiten (fliissige Kristalle) 86-88, 151.

-, flow problems, Stromungsprobleme 473 to 475·

-, hyperelasticity, Hyperelastizitiit 314 to 316.

-, stored energy, gespeicherte Energie 315. Superimposed elastic strain (theorem), iiber

lagerte elastische Verzerrung (Satz) 250. Superstability, Uberstabilitiit 255, 257. Swelling at exit from a pipe, Schwell-Effekt

am Rohrenausgang 455-458. Symbols, index of, 5 ymbole, Verzeichnis 17

to 19.

T-E inequalities (tension-extension), Spannungs-Dehnungs- Ungleichungen 155.

Temperature, Temperatur 133, 294. Temperature relation, Temperaturbeziehung

297, 301, 361. Tensor components, Tensorkomponenten 14. Tensor of deformation see deformation grad

ient, Deformationstensor s. Deformationsgradient.

Tensor function, definition, Tensorfunktion, Definition 21. -, linear, lineare 22, 23. - of one variable, einer Variablen 32 to 35.

Tensor polynomial, Tensorpolynom 21. Tensor power series, Tensorpotenzreihe 21. Thermal constraints, thermische Zwangs-

bedingungen 329. Thermal equilibrium in a simple material,

Thermisches Gleichgewicht in einer einfachen Substanz 298-301.

Thermodynamic process, thermodynamischer ProzefJ 295.

Thermodynamics of diffusion, Thermodynamik der Diffusion 541. of irreversible processes, irreversibler Prozesse 373. of simple materials, einfacher 5ubstanzen 363-381.

Thermo-elasticity, Thermoelastizitiit 355 to 363.

- with linear viscosity, mit linearer Viskositiit 357.

Thermomechanical potential, thermomechanisches Potential 299.

Thermostatic limit theorem, thermostatischer Grenzwertsatz 371.

Thermostatics of simple materials, Thermostatik einfacher Substanzen 300.

Subject Index. 601

Time-dependent deformations of tubes, zeitabhiingige Deformation von Rohren 212seq.

Time derivatives, material and spatial, Zeitableitungen, materielle und riiumliche 39.

Time-lapse, natural, Zeitablauf, naturlicher 437.

Torque in cone-and-plate flow, Drehmoment bei Stromung zwischen Kegel und Platte 463. in Couette flow, in der Couette-Stromung 449.

Torsion of a cylinder, Torsion eines Zylinders 191-193, 343seq., 352seq.

-, second-order theory, Theorie zweiter Ordnung 232-237.

- of a tube, eines Rohres 191-193, 232 to 237.

-, wrong theories, falsche Theorien 236. Torsional flow, Torsionsstromung 458-464. Torsional rigidity, Torsionsstarrheit 266. TOUPIN'S electromechanical theories, Toupins

elektromechanische Theorien 385-389. TOUPIN'S oriented hyperelastic materials,

Toupins orientierte hyperelastische Substanzen 391-397.

Trace of a tensor, Spur eines Tensors 15, 23 seq.

- --, its gradient, ihr Gradient 25. Transpose of a tensor, Transponierte eines

Tensors 15. Transverse isotropy, transversale I sotropie

82. Transverse wave, Transversalwelle 268, 280. Transversely isotropic fluids of ERICKSEN,

transversal isotrope Flussigkeiten von Ericksen 527-528.

Triclinic solids, trikline F estkorper 85. Tube see also pipe. Tube, inflation and bending, Dehnen und Bie

gen eines Rohres 189-195, 212seq., 343. -, non circular, flow through it, Stromung

durch ein nicht kreisformiges Rohr 468 to 471.

--, radial oscillations, Radialschwingungen eines Rohres 354.

--, secondary flow, sekundiire Stromung in einem Rohr 497-504.

-, torsion and extension, Torsion und Dehnung eines Rohres 232-237, 353.

--, various deformations, verschiedene Deformationen eines Rohres 353.

Undistorted state of a solid, unverzerrter Zustand eines Festkorpers 85.

- - of a subfluid, einer anisotropen Flussigkeit 87.

Undistorted states of an isotropic material, unverzerrte Zustiinde eines isotropen M aterials 78, 82, 139, 151.

Uniform dilatation, gleichformige Dilatation 173.

Uniform reference, gleichmiif3ige Bezugsgesamtheit 89.

Uniqueness, its failure, Eindeutigkeit, ihr Versagen 128seq.

Uniqueness theorem of ERICKSEN and TouPIN, Eindeutigkeitssatz von Ericksen und Toupin 255. - for free vibrations, fiir freie Schwingungen 256. - for potential deformations, fur Potentialdeformationen 165. - of SIGNORINI, von Signorini 225. - of TRUESDELL and TOUPIN, von Trues-dell und Toupin 249.

Unit tensor, Einheitstensor 23.

Variational principles for hyperelastic materials, Variationsprinzipien fur hyperelastische Substanzen 326-328.

Vector components, Vektorkomponenten 14. Velocity field, Geschwindigkeitsfeld 39. Velocity profile of channel flow, Geschwindig-

keitsprofil einer Kanalstromung 444. - - of Poiseuille flow, der Poiseuille

Stromung 452. Vibrations, infinitesimal, uniqueness theorem,

infinitesimale Schwingungen, Eindeutigkeitssatz 256.

Virtual work, virtuelle A rbeit 306. Visco-elasticity, classical theory, Visko

elastizitiit, klassische Theorie 116. -, linear, lineare 109, 378. Visco metric flow, viskometrische Stromung

432, 435-440. -, asymptotic theory, asymptotische Theorie 488-490. - of ERICKSEN'S anisotropic fluids, der anisotropen Flussigkeiten von Ericksen 533-537-

Viscometric functions, viskometrische Funktionen 13,426, 495, 504.

- - for poly-isobutyl ene, fiir Poly-isobutylen 467seq.

Viscometry, theories, Viskometrie, Theorien 465-468.

Viscosity, Viskositiit 65. -, classical theory, klassische Theorie 113 to

117. Viscosity function, Viskositiitsfunktion 436. Viscosity, natural, Viskositiit, natiirliche

437. Volume discharge in channel flow, Durchsatz

bei Kanalstromung 444. - in flow between coaxial pipes, bei Stromung zwischen koaxialenRohrleitungen 451. - of Poiseuille flow, bei PoiseuilleStromung 452.

Volume change in second-order theory, Volumiinderung in der Theorie zweiter Ordnung 240, 346.

WANG'S theories of fading memory, Wangsche Theorien des schwindenden Gediichtnisses 105,112-113.

602 Subject Index.

Wave propagation, Wellenausbreitung 267 to 294, 332-335.

- - in materials with memory, in Substanzen mit Gediichtnis 382-385.

'Naves see also acceleration waves, Wellen s. auch Beschleunigungswellen. of finite amplitude, endlicher Amplitude 283 seq. of higher order, hoherer Ordnung 272seq., 283.

-, homentropic and homothermal, homentrope und homotherme 272,335, 383seq.

- in incompressible materials, in inkompressiblen Substanzen 291-294.

- in isotropic materials, in isotropen Substanzen 278-291.

-, plane infinitesimal, ebene infinitesimale 273-278.

WEISSENBERG'S assertion, Weissenbergsche A ussage 484.

Weissenberg effect, Weissenberg-Effekt 453 seq.

Work done during a homogeneous deformation, A rbeitsleistung bei einer homogenen Deformation 299.

Work theorems for elastic materials, Arbeitssiitze fur elastische Substanzen 304-307. in hypo-elasticity, der H ypoelastizitiitstheorie (411-413.

Yield in hypo-elasticity, FliefJen in der Hypoelastizitiitstheorie 420-426.

ZENER'S formula for second-order change of volume, Zenersche Formel fur Volumiinderung in zweiter Niiherung 346.

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