Scaling of Effective Moduli of Generalised Continua

We model materials with self-similar structure by a set of continua, C-H, 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 alpha, the Cosserat moduli scale with exponents alpha and alpha + 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.