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A Historical Perspective of Generalized Continuum Mechanics

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Mechanics of Generalized Continua

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 7))

Abstract

In a period of forty years the author has had the opportunity to work, or to entertain friendly connections, with many actors of the scene of generalized continuum mechanics (GCM). This training and knowledge here is used to the benefit of the readers as an overview of this scene with the aim to delineate further avenues of development within the framework of the trilateral seminar held in Wittenberg (2010). Starting essentially with Pierre Duhem and the Cosserat brothers, this specialized, albeit vast, field of continuum mechanics has developed by successive abandonments of the working hypotheses at the basis of standard continuum mechanics, that mechanics masterly devised by Euler and Cauchy and some of their successors in the 19th century (Piola, Kirchhoff, etc.). In the present survey we briefly analyze successive steps such as the introduction of nonsymmetric stresses, couple stresses, internal degrees of freedom and microstructure, the introduction of strain gradient theories, and material inhomogeneities with a length scale, nonlocality of the weak and strong types, the loss of Euclidean geometry to describe the material manifold, and finally the loss of classical differentiability of basic operations as can occur in a deformable fractal material object.

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  1. Université Pierre et Marie Curie – Paris 6, Institut Jean Le Rond d’Alembert, UMR CNRS 7190, 4 place Jussieu, 75252, Paris Cedex 05, France

    Gérard A. Maugin

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  1. Halle-Wittenberg, Zentrum für Ingenieurwissenschaften, Martin-Luther-Universität, Kurt-Mothe-Str. 1, Halle (Saale), 06099, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. , Institut Jean Le Rond d’Alembert, UPMC (Paris), Tour 55, Place Jussieu 4, Paris Cedex 05, 75252, France

    Gérard A. Maugin

  3. IMASH RAN, Belinskogo str. 85, Nizhny Novgorod, 603024, Russian Federation

    Vladimir Erofeev

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Maugin, G.A. (2011). A Historical Perspective of Generalized Continuum Mechanics. In: Altenbach, H., Maugin, G., Erofeev, V. (eds) Mechanics of Generalized Continua. Advanced Structured Materials, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19219-7_1

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