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Continuum Mechanics of Fractal Media

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Encyclopedia of Continuum Mechanics

Synonyms

Approaches to the description of fractal media; Continuum models of fractal media; Fractal continuum mechanics

Definitions

Basic methods and approaches to the description of fractal media and distributions in continuum mechanics

Introduction

Fractal is a measurable metric set that, in general, cannot be considered a linear (vector) space (Falconer, 1985; Feder, 1988). One of the most important characteristic properties of fractals is their non-integer dimensions (Falconer, 1985; Feder, 1988) such as the Hausdorff and box-counting dimensions. In accordance with the definition of the Hausdorff dimension (and the box-counting dimension), the diameter of the covering sets should tend to zero. The fractal structure of real media cannot be observed at all scales. The fractal properties of fractal media are observed only in a certain range of scales. The fractal structure exists only for the scales L > L 0, where L 0is the characteristic size of atoms or molecules of fractal media....

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Author information

Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia

    Vasily E. Tarasov

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  1. Vasily E. Tarasov
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Correspondence to Vasily E. Tarasov .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana–Champaign, 1206 West Green Street, 61801, Urbana, IL, USA

    Martin Ostoja-Starzewski

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Tarasov, V.E. (2018). Continuum Mechanics of Fractal Media. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_69-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_69-1

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