Paper number 215


V. G. Oshmyan, S. A. Patlazhan, S. A. Timan

Department of Polymer and Composite Materials, N.N. Semenov Institute of Chemical Physics, 4 Kosygin St., Moscow 117977, Russia.

Summary Elastic scaling behavior of a continuous anisotropic fractal, 2D Sierpinski carpet, is the subject of the study. In the case of porous in elastic matrix, P. Sheng and R. Tao and S. A. Patlazhan have found that axial and shear moduli of the carpet exhibit distinct scaling with the size of the system. However, it is widely accepted that different stiffness of isotropic fractals scale with equal exponents. The nature of such discrepancy has remained unclear. Using numerical position-space renormalization group technique, we show that different stiffness of the carpet also scale with equal exponents. In particular, it means that both in the cases of porous and rigid inclusions fractal Poisson ratio has non zero values independent of matrix moduli. Difference in the values of scaling exponents obtained in previous study is caused by analysis of the initial fractal generations.
Keywords elasticity, fractal, scaling, renormalization, disordered composite.

Theme : Fibres ; Glass and Carbon Fibres

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