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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
El Mamouni Anass and El Omri Abderrahim
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DOI:10.17265/2161-6221/2018.9-10.005
Civil Engineering and Mechanic Lab Science and Technic Faculty, Tangier
This work is related to bounding the effective conductivity of an isotropic two-phase fibrous periodical composite. These well known bounds are classically obtained for any inclusion shape by the fourier method. So, they can be expressed only in the Fourier space. A real formulation of the solution of the periodical conductivity problem based on the discrete Radon transform has been recently proposed. The use of this framework leads us here to a simple and explicit real bounds for effective properties. The effect of the microstructure is hence more evidenced. It is also shown here that the obtained bounds coincide with the classical Hashin Shtrikmann bounds when the microstructure has some specific symmetry.
Homogenization, finite radon transform, Hashin-Shtrikman bounds, periodical media, symmetric, heterogeneous conductivity, fibrous media.