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Mechanics of Generalized Continua pp 3–13Cite as

Generalized Continuum Mechanics: What Do We Mean by That?

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Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 21))

Abstract

Discursive historical perspective on the developments and ramifications of generalized continuum mechanics from its inception by the Cosserat brothers (Théorie des corps déformables. Hermann, 1909) with their seminal work of 1909 to the most current developments and applications is presented. The point of view adopted is that generalization occurs through the successive abandonment of the basic working hypotheses of standard continuum mechanics of Cauchy, that is, the introduction of a rigidly rotating microstructure and couple stresses (Cosserat continua or micropolar bodies, nonsymmetric stresses), the introduction of a truly deformable microstructure (micromorphic bodies), “weak” nonlocalization with gradient theories and the notion of hyperstresses, and the introduction of characteristic lengths, “strong nonlocalization” with space functional constitutive equations and the loss of the Cauchy notion of stress, and finally giving up the Euclidean and even Riemannian material background. This evolution is paved by landmark papers and timely scientific gatherings (e.g., Freudenstadt, 1967; Udine, 1970, Warsaw, 1977).

Preliminary note: Over 40 years, the author has benefited from direct studies under, and lectures from, P. Germain, A.C. Eringen, E.S. Suhubi, R.D. Mindlin, W. Nowacki, V. Sokolowski, S. Stojanovic, from contacts with J.L. Ericksen, C.A. Truesdell and D.G.B. Edelen, from friendship with C.B. Kafadar, J.M. Lee, D. Rogula, H.F. Tiersten, J. Jaric, P.M. Naghdi, I.A. Kunin, L.I. Sedov, V.L. Berdichevskii, E. Kröner, and most of the authors in the present volume as co-workers or friends, all active contributors to the present subject matter. He apologizes to all these people who certainly do not receive here the fully deserved recognition for their contribution to the field.

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  1. UMR 7190 CNRS, Institut Jean Le Rond d’Alembert, UPMC Univ Paris 6, Paris, France

    Gérard A. Maugin

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  1. Institut Jean Le Rond d'Alembert, Université Paris VI, place Jussieu 4, Paris CX 5, 75252, France

    Gérard A. Maugin

  2. Faculty of Civil Engineering and, Delft University of Technology,, Stevinweg 1, Delft, 2628 CN, Netherlands

    Andrei V. Metrikine

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Maugin, G.A. (2010). Generalized Continuum Mechanics: What Do We Mean by That?. In: Maugin, G., Metrikine, A. (eds) Mechanics of Generalized Continua. Advances in Mechanics and Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5695-8_1

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