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Scaling of Effective Moduli of Generalised Continua

  • A.V. Dyskin
  • E. Pasternak
Conference paper
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)

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.

Keywords

Self-similar approximation fractal approximation Cosserat continuum effective characteristics 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • A.V. Dyskin
    • 1
  • E. Pasternak
  1. 1.School of Civil and Resource EngineeringThe University of Western AustraliaCrawleyAustralia

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