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Homogenization Methods and Generalized Continua in Linear Elasticity

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Encyclopedia of Continuum Mechanics

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Synonyms

Homogenization method :

The homogenization method is an upscaling method that proceeds from microscale to macroscale. In place of homogenized behavior, one can equivalently use macroscopic behavior, effective behavior, or upscaled behavior.

Generalized continua :

The term “generalized continua” could be replaced by enriched continua or enhanced continua. This notion encompasses several types of non-Cauchy behavior, as Cosserat media, strain gradient or higher gradient media, micromorphic material, etc. In dynamics, metamaterials and inner resonance materials also correspond to generalized continua.

Definition

Homogenization method :

The homogenization method used in this entry is the upscaling two-scale asymptotic method of periodic media. It applies in statics and dynamics and provides, in situation of scale separation, the macroscopic behavior of the microstructured (discrete or continuous) medium, at the leading order but also at the higher orders through correctors. The...

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Acknowledgements

This entry benefited from many scientific exchanges with number of colleagues, among which I would like to address special thanks to J.L. Auriault, G. Bonnet, D. Caillerie, C. Chesnais, F. dell’Isola, S. Forest, S. Hans, D. Lafarge, G. Maugin†,V. Montchiet, A. Rallu, K. Sab, L. Schwan, J. Soubestre, and R. Venegas.

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  1. LGCB/LTDS – CNRS UMR 5513, Ecole Nationale des Travaux Publics de l’Etat – Université de Lyon, Vaulx-en-Velin, France

    Claude Boutin

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  1. Claude Boutin
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Correspondence to Claude Boutin .

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  1. Lehrstuhl Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Fakultät für Maschinenbau, Esslingen University of Applied Sciences, Esslingen, Germany

    Andreas Öchsner

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Boutin, C. (2020). Homogenization Methods and Generalized Continua in Linear Elasticity. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55771-6_112

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