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”.
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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)
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)
Altenbach, H., Maugin, G.A., Erofeeev, V. (eds.): Mechanics of Generalized Continua. Springer-Verlag, Berlin (2011)
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)
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)
Cosserat, E., Cosserat, F.: Théorie des corps déformables. Hermann, Paris [Reprint, Gabay, Paris, 2008] (1909)
Cowin, S.C., Nunziato, J.W.: Linear elastic materials with voids. J. Elasticity 13, 125–147 (1983)
Duhem, P.: Le potentiel thermodynamique et la pression hydrostatique. Ann. Ecol. Norm. Sup. 10, 187–230 (1893)
Eringen, A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1–18 (1966)
Eringen, A.C.: Micropolar fluids with stretch. Int. J. Engng. Sci. 7, 115–127 (1969)
Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002)
Eringen, A.C., Edelen, D.G.B.: On nonlocal elasticity. Int. J. Egng. Sci. 10(3), 233–248 (1972)
Eringen A.C., Maugin G.A.: Electrodynamics of continua. Two volumes, Springer-Verlag, New York (Soft cover reprint, 2012] (1990)
Eringen, A.C., Suhubi, E.S.: Nonlinear theory of simple microelastic solids I. Int. J. Eng. Sci. 2, 189–203 (1964)
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)
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)
Kröner, E.: Kontinuumstheorie der Versetzungen und Eigenspannungen. Springer-Verlag, Berlin (1958)
Kröner, E. (Ed., 1968). Generalized Continua (Proc.IUTAM Symp. Freudenstadt, 1967). Springer-Verlag, Berlin
Kröner, E., Datta, B.K.: Nichtlokal Elastostatik: Ableitung aus der Gittertheorie. Z. Phys. 196, 203–211 (1966)
Kunin, I.A.: Model of elastic medium with simple structure and space dispersion. Prikl. Mat. Mekh. 30, 542–550 (1966)
Kunin, I.A.: Elastic Media with Microstructure I & II. Springer-Verlag, Berlin, (translation from the 1975 Russian edition, edited by E. Kröner) (1982)
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)
Le Roux, J.: Recherches sur la géométrie des déformations finies. Ann. Ecole Norm. Sup. 30, 193–245 (1913)
Maugin, G.A.: The method of virtual power in continuum mechanics: application to coupled fields. Acta Mech. 35, 1–70 (1980)
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)
Maugin, G.A.: Configurational Forces: Thermomechanics, Physics, Mathematics and Numerics. CRC/Chapman & Hall/Taylor, Francis, Boca Raton, FL (2011)
Maugin, G.A.: Generalized continuum mechanics: Various paths, Chapter 13. In: G.A. Maugin (ed.) Continuum Mechanics Through the Twentieth Century. Springer, Dordrecht (2013)
Maugin, G.A., Metrikine, A.V. (eds.): Mechanics of Generalized Continua: One Hundred Years After the Cosserats. Springer, New York (2010)
Mindlin, R.D.: Microstructure in linear elasticity. Arch. Rat. Mech. Anal. 16, 51–78 (1964)
Mindlin, R.D., Eshel, N.N.: On the first strain gradient theories in linear elasticity. Int. J. Solids Structures 4, 109–124 (1968)
Mindlin, R.D., Tiersten, H.F.: Effects of couple stresses in linear elasticity. Arch. Rat. Mech. Anal. 11, 415–448 (1962)
Noll, W.: Materially Uniform Simple Bodies with Inhomogeneities. Arch. Rat. Mech. Anal. 27, 1–32 (1967)
Rogula, D.: Influence of spatial acoustic dispersion on dynamical properties of dislocations. Bull. Acad. Pol. Sci. Sér. Sci. Techn. 13, 337–385 (1965)
Stojanovic, R.: Mechanics of Polar Continua. CISM Lectures, Udine, Italy (1969)
Toupin, R.A.: Elastic materials with couple stress. Arch. Rat. Mech. Anal. 11, 395–414 (1962)
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)
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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
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