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IUTAM Symposium on Scaling in Solid Mechanics pp 189–198Cite as

Scaling of Effective Moduli of Generalised Continua

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Abstract

We model materials with self-similar structure by a set of continua, CH, each representing the original material with all structural elements of sizes smaller than H. We then continue this sequence in a self-similar manner to H→ 0. The intersection of these continua gives a fractal F where all fields scale according to the power law. By considering scaling of the energy in linear elastic Cosserat continuum we find that if the classical elastic moduli scale with an exponent α, the Cosserat moduli scale with exponents α and α+2. Using this rule, we determine the dispersion relations for travelling waves and find the full set of the exponents for the cases of material with cracks and pores.

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Author information

Authors and Affiliations

  1. School of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

    A.V. Dyskin

Authors
  1. A.V. Dyskin
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  2. E. Pasternak
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Editor information

Editors and Affiliations

  1. School of Engineering, Cardiff University, Queen’s Bldg., The Parade, Cardiff CF24 3AA, UK

    F.M. Borodich (borodichfm@cardiff.ac.uk) (borodichfm@cardiff.ac.uk)

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Dyskin, A., Pasternak, E. (2009). Scaling of Effective Moduli of Generalised Continua. In: Borodich, F. (eds) IUTAM Symposium on Scaling in Solid Mechanics. Iutam Bookseries, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9033-2_18

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  • DOI: https://doi.org/10.1007/978-1-4020-9033-2_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9032-5

  • Online ISBN: 978-1-4020-9033-2

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