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Nonlinear Micropolar Elasticity

  • R. Stojanovic
Part of the International Centre for Mechanical Sciences book series (CISM, volume 151)

Abstract

The Cosserat continuum is a material continuum with “points” which may rotate independently of the displacements. A better interpretation of this continuum is offered through the assignment of rigid triads of vectors to the points, and admitting the triads to rotate independently of the points of the medium.

Keywords

Stress Tensor Constitutive Relation Couple Stress Antisymmetric Part Cosserat Continuum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    E. and F. Cosserat: “Sur la mécanique générale”, C. R. Acad. Sc. Paris, 145, 1139–1142 (1907).Google Scholar
  2. [2]
    E. and F. Cosserat: “Sur la théorie des corps minces”, C.R. Acad. Sci. Paris, 146, 169–172 (1908).MATHGoogle Scholar
  3. [3]
    E. and F. Cosserat: “La théorie des corps déformables”, Paris (1909).Google Scholar
  4. [4]
    J.L. Ericksen and C. Truesdell: “Exact theory of stress and strain in rods and shells”, Arch. Rat. Mech. Analysis 1, 295–323 (1958).ADSCrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    J. Sudria: “L’action euclidienne de déformation et de mouvement”, Mem. Sc. Physique, 29, Paris (1935).Google Scholar
  6. [6]
    E. Kroner: “Kontinuumstheorie der Versetzungen und Eigenspannungen”, Ergeb. Angew. Math., 5, Berlin-Gottingen-Heidelberg, (1958).Google Scholar
  7. [7]
    W. Gunther: “Zur Statik und Kinematik des Cosseratschen Kontinuums”, Abh. Braunschw. Wiss. Ges. 10, 195–213 (1958).Google Scholar
  8. [8]
    H. Schafer: “Versuch einer Elastizitatstheorie der zweidimensionalen ebenen Cosserat-Kontinuums”, Miszellaneen der angew. Mech., Festschrift W. Tolmien, 277–292, Berlin (1962).Google Scholar
  9. [9]
    S. C. Cowin: “Mechanics of Cosserat continua”, Doct. Diss. Pennsylvania State Univ., (1962).Google Scholar
  10. [10]
    E.L. Aero and E. V. Kuvshinskii: “Osnovnie uravnenia teorii uprugosti sred s vrashchatal’nim vzaimodeistviem chastic”, Fiz. Tv. Tela 2, 1399–1409, (1960).Google Scholar
  11. [11]
    C. Truesdell and R. Toupin: “The classical field theories”, Handb. der Phys. (ed. S. Flügge), Bd. III/1, Berlin-Götting. -Heidelberg, (1960).Google Scholar
  12. [12]
    G. Grioli: “Elasticità asimmetrica”, Ann. di Mat. Pura ed Appl., Ser. 1V, 50, 389–417 (1960).CrossRefMATHMathSciNetGoogle Scholar
  13. [13]
    R. Toupin: “Elastic materials with couple-stresses”, Arch. Rat. Mech. Anal. 11, 385–414. (1962).CrossRefMATHMathSciNetGoogle Scholar
  14. [14]
    E. V. Kuvshinskii, E.L. Aero: “Kontinual’naja teoria asimetricheskoi uprugosti. Uchet ”vnutrennego“ vrashchenia”, Fiz. Tv. Tela 5, 2591–2598 (1963).Google Scholar
  15. [15]
    R. Toupin: “Theories of elasticity with couple-stresses” Arch. Rat. Mech. Anal. 17, 85–112 (1964).CrossRefMATHMathSciNetGoogle Scholar
  16. [16]
    A. C. Eringen: “Theory of micropolar continua”, Proc. 9th Midwestern Mech. Conference, Madison, Wisconsin (1965).Google Scholar
  17. [17]
    A. C. Eringen and E.S. Suhubi: “Nonlinear theory of simple microelastic solids”, Int. J..Engng. Sc., 2, 189–203 (1964).CrossRefMATHMathSciNetGoogle Scholar
  18. [18]
    R. Stojanovic and S. Djuric: “On the measures of strain in the theory of the elastic generalized Cosserat continua”, Symposia Mathematics 1, 211–228, (1968).Google Scholar
  19. [19]
    R. Stojanovic: “Mechanics of Polar Continua”, CISM, Udine, (1969).Google Scholar
  20. [20]
    C. B. Kafadar and A. C. Eringen: “Micropolar media-I. The classical theory”, Int. J. Eng. Sc., 9, 271–305 (1971).CrossRefMATHGoogle Scholar
  21. [21]
    R. Toupin: “The elastic dielectric”, J. Rat. Mech. Anal. 5, 849–915 (1955).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1974

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  • R. Stojanovic

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