From Material Point to Cosserat Fiber bundle. Development of Ideas

• Autorzy: Povstenko, J.
• Języki publikacji: EN

Słowa kluczowe

PL

ciągłość mikrostruktury; analiza matematyczna; funkcje punktów ciągłych

EN

continuity of the microstructure; mathematical analysis; continuous point functions

• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 1999
• Tom: Vol. 6
• Strony: 85--93
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Povstenko, J.

• Pedagogical University Institute of Mathematics Al. Armii Krajowej 13/15 Częstochowa 42-201

Bibliografia

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• [2] Badur J., Povstenko Y.Z., On two reinterpretations of Cosserat continuum: fibet bundle versus the motor calculus ,Arch. Mech. 50 (1998), 367-376.
• [3] Cosserat E., Cosserat F., Tlieorie des corps deformables, Hermann, Paris, 1909.
• [4] Duhem P., Le potentiel thermodynamique et la pression hydrostatique, Ann. Ecole Norm. (3) 10 (1893), 187-230.
• [5] Edelen D.G.B., Lagoudas D.C., Gauge Theory of Defects in Solide. North Holland, Amsterdam, 1988.
• [6] Ericksen J .1., Kinematics of macromolecules, Arch. Ration. Mech. Anal. 9 (1962), 1-8.
• [7] Ericksen J .L., Hydrostatic theory of liquid crystals, Arch. Ration. Mech. Anal. 9 (1962),379-394.
• [8] Eringen A.C., Simple microf1uids, Int. J. Engng. Sci, 2 (1964),205- 217.
• [9] Eringen A.C., Suhubi E.S., Nonlinear theory of simple microelastic solids, Int. J. Engng. Sci. 2 (1964), 189-204.
• [10] Eringen A.C., Suhubi E.S., Nonlinear theory of simple microelastic solids, Int. J. Engng. Sci, 2 (1964), 389-404.
• [11] Green A.E., Rivlin R.S., Simple force and stress multipoles, Arch. Rational Mech. Anal, 16 (1964),325-353.
• [12] Green A.E., Rivlin R.S., Multipolec continuum mechanics, Arch. Rational Mech. Anal. 17 (1964),113-147.
• [13] Kadic A., Edelen D.G.B., A gauge theory of dislocations and disclutetions, Lecture Notes in Physics No 174, Springer, Berlin, 1983.
• [14] Kordos M., Włodarski L., O geometrii dla postronnych, PWN, Warszawa, 1981.
• [15] Lagoudas D.C., A gauge theory of defects in media with microstructure, Int. J. Engng. Sci, 27 (1989),237-249.
• [16] Marsden J.E., Hughes T.J.R, Mathematical Foundations ofElasticity, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1983.
• [17] Mindlin R.D., Microstructure in linear elssiicity, Arch. Rational Mech. Anal. 16 (1964), 51-78.
• [18] Nash C., Sen S., Topology and Geometry for Physicists, Academic Press, London, 1983.
• [19] Sansour C., A unified concept of elestic-viecoplestic Cosserat and micromorphic continua, Proc. 2nd European Mechanics of Materials Conference on Mechanics of Materials wit h Intrinsic Length Scale: Physics, Experiments, Modelling, and Applications, Magdeburg, Germany, February, 23-26, 1998, 339-346.
• [20] Sedov L.I., Tsypkin A.G., Fundamentals of Macroscopic Theories of Gravitation and Electromagnetizm, Nauka, Moscow, 1989. (In Russian).
• [21] Toupin RA., Theories of elasticity with couple-stresses, Arch. Ratlon. Mech. Anal. 17 (1964),85-112.
• [22] Truesdell C., Toupin R., The Classical Field Theories. Handbuch der Physik, III/l, Springer, Berlin, 1960.
• [23] Truesdell C., Noll W., The Non-Lineer Field Theories of Mechanics. Handbuch der Physik, III/3, Springer, Berlin, 1965.
• [24] Von Westenholz C., Differential Forms in Mathematical Physics, North- Holland Publ., Amsterdam, 1978.