Skip to main content

What Is Generalized Continuum Mechanics (GCM)?

  • Chapter
  • First Online:
Non-Classical Continuum Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 51))

Abstract

We classify under the title “generalized continuum mechanics” all what is not covered in the restricted framework of the Cauchy model exposed in the prerequisite Chap. 1 under the title of “classical continuum mechanics”.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Altenbach, H., Eremeyev, V.A. (eds.): Generalized Continua—from the Theory to Engineering Applications (Text of lectures at the CISM, Udine, 2012). Springer, Wien (2013)

    Google Scholar 

  • Altenbach, H., Forest, S., Krivstsov, A. (eds.): Generalized Continua as Models for Materials (with Multi-Scale Effects or Under Multi-Field Actions). Springer-Verlag, Berlin (2013)

    Google Scholar 

  • Altenbach, H., Maugin, G.A., Erofeeev, V. (eds.): Mechanics of Generalized Continua. Springer-Verlag, Berlin (2011)

    MATH  Google Scholar 

  • Barré de Saint-Venant, A.: Note sur les valeurs que prennent les pressions dans un corps solide isotrope lorsque l’on tient compte des dérivées d’ordre supérieur des déplacements très petits que leurs points ont prouvés. C. R. Acad. Sci. Paris 68, 569–571 (1869)

    MATH  Google Scholar 

  • Bilby, B.A., Bullough, R., Smith, E.: Continuous distributions of dislocations: new application of the methods of non-Riemannian geometry. Proc. Roy. Soc. Lond. A231, 263–273 (1955)

    Article  MathSciNet  Google Scholar 

  • Cosserat, E., Cosserat, F.: Théorie des corps déformables. Hermann, Paris [Reprint, Gabay, Paris, 2008] (1909)

    Google Scholar 

  • Cowin, S.C., Nunziato, J.W.: Linear elastic materials with voids. J. Elasticity 13, 125–147 (1983)

    Article  MATH  Google Scholar 

  • Duhem, P.: Le potentiel thermodynamique et la pression hydrostatique. Ann. Ecol. Norm. Sup. 10, 187–230 (1893)

    MathSciNet  MATH  Google Scholar 

  • Eringen, A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  • Eringen, A.C.: Micropolar fluids with stretch. Int. J. Engng. Sci. 7, 115–127 (1969)

    Article  MATH  Google Scholar 

  • Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002)

    MATH  Google Scholar 

  • Eringen, A.C., Edelen, D.G.B.: On nonlocal elasticity. Int. J. Egng. Sci. 10(3), 233–248 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  • Eringen A.C., Maugin G.A.: Electrodynamics of continua. Two volumes, Springer-Verlag, New York (Soft cover reprint, 2012] (1990)

    Google Scholar 

  • Eringen, A.C., Suhubi, E.S.: Nonlinear theory of simple microelastic solids I. Int. J. Eng. Sci. 2, 189–203 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  • Germain, P.: La méthode des puissances virtuelles en mécanique des milieux continus, Première partie: théorie du second gradient. J. de Mécanique (Paris) 12, 235–274 (1973)

    MathSciNet  MATH  Google Scholar 

  • Kondo K.: Non-Riemannian geometry of imperfect crystals from a macroscopic viewpoint. In: Kondo, K. (ed.) RAAG Memoirs of the Unifying Study of Basic Problems in Engineering and Physical Sciences by Means of geometry, vol. 1, pp. 459–480. Gakujutsu Bunken Fukyukai, Tokyo (1955)

    Google Scholar 

  • Kröner, E.: Kontinuumstheorie der Versetzungen und Eigenspannungen. Springer-Verlag, Berlin (1958)

    Book  MATH  Google Scholar 

  • Kröner, E. (Ed., 1968). Generalized Continua (Proc.IUTAM Symp. Freudenstadt, 1967). Springer-Verlag, Berlin

    Google Scholar 

  • Kröner, E., Datta, B.K.: Nichtlokal Elastostatik: Ableitung aus der Gittertheorie. Z. Phys. 196, 203–211 (1966)

    Article  Google Scholar 

  • Kunin, I.A.: Model of elastic medium with simple structure and space dispersion. Prikl. Mat. Mekh. 30, 542–550 (1966)

    Google Scholar 

  • Kunin, I.A.: Elastic Media with Microstructure I & II. Springer-Verlag, Berlin, (translation from the 1975 Russian edition, edited by E. Kröner) (1982)

    Google Scholar 

  • Le Roux, J.: Etude géométrique de la torsion et de la flexion, dans les déformations infinitésimales d’un milieu continu. Ann. Ecole Norm. Sup. 28, 523–579 (1911)

    MathSciNet  MATH  Google Scholar 

  • Le Roux, J.: Recherches sur la géométrie des déformations finies. Ann. Ecole Norm. Sup. 30, 193–245 (1913)

    MathSciNet  MATH  Google Scholar 

  • Maugin, G.A.: The method of virtual power in continuum mechanics: application to coupled fields. Acta Mech. 35, 1–70 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  • Maugin, G.A.: Generalized continuum mechanics: what do we understand by that? In: Maugin, G.A., Metrikine, A.V. (eds.) Mechanics of Generalized Continua: One Hundred Years After the Cosserats, pp. 3–13. Springer, New York (2010)

    Chapter  Google Scholar 

  • Maugin, G.A.: Configurational Forces: Thermomechanics, Physics, Mathematics and Numerics. CRC/Chapman & Hall/Taylor, Francis, Boca Raton, FL (2011)

    Google Scholar 

  • Maugin, G.A.: Generalized continuum mechanics: Various paths, Chapter 13. In: G.A. Maugin (ed.) Continuum Mechanics Through the Twentieth Century. Springer, Dordrecht (2013)

    Google Scholar 

  • Maugin, G.A., Metrikine, A.V. (eds.): Mechanics of Generalized Continua: One Hundred Years After the Cosserats. Springer, New York (2010)

    MATH  Google Scholar 

  • Mindlin, R.D.: Microstructure in linear elasticity. Arch. Rat. Mech. Anal. 16, 51–78 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  • Mindlin, R.D., Eshel, N.N.: On the first strain gradient theories in linear elasticity. Int. J. Solids Structures 4, 109–124 (1968)

    Article  MATH  Google Scholar 

  • Mindlin, R.D., Tiersten, H.F.: Effects of couple stresses in linear elasticity. Arch. Rat. Mech. Anal. 11, 415–448 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  • Noll, W.: Materially Uniform Simple Bodies with Inhomogeneities. Arch. Rat. Mech. Anal. 27, 1–32 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  • Rogula, D.: Influence of spatial acoustic dispersion on dynamical properties of dislocations. Bull. Acad. Pol. Sci. Sér. Sci. Techn. 13, 337–385 (1965)

    Google Scholar 

  • Stojanovic, R.: Mechanics of Polar Continua. CISM Lectures, Udine, Italy (1969)

    Google Scholar 

  • Toupin, R.A.: Elastic materials with couple stress. Arch. Rat. Mech. Anal. 11, 395–414 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, C.C.: On the geometric structure of simple bodies, a Mathematical foundation for the theory of continuous distributions of dislocations. Arch. Rat. Mech. Anal. 27, 33–94 (1967)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gérard A. Maugin .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Nature Singapore Pte Ltd

About this chapter

Cite this chapter

Maugin, G.A. (2017). What Is Generalized Continuum Mechanics (GCM)?. In: Non-Classical Continuum Mechanics. Advanced Structured Materials, vol 51. Springer, Singapore. https://doi.org/10.1007/978-981-10-2434-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-2434-4_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2433-7

  • Online ISBN: 978-981-10-2434-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics