Abstract
The present paper derives numerical bounds of the elastic properties of polycrystals. The homogenized elastic coefficients are computed from Voronoi-type unit cells. The main result of the article detemines the upper and lower bounds for a case of polycrystals made up of cubic single crystals by using the fast Fourier transform method (FFT) based on the shape function. Our method guarantees the exact solutions in comparison to the Moulinec and Suquet’s method within some uncontrolled approximations. The proposed method could be extended to account for other material symmetries such as hexagonal or tetragonal crystals.
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