First-principles approach for effective elastic-moduli calculation: Application to continuous fractal structure

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Abstract
We present a new first-principles approach to the calculation of effective elastic moduli of composites based on the iterative solution of the Dyson equation for elastic wave scatterings in inhomogeneous media. Application of the method to the examination of elastic scaling behavior of a continuous fractal shows that the moduli associated with different elastic eigenmodes exhibit distinct exponents in scaling with the size of the system.

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