FFT, DA, and Mori-Tanaka approximation to determine the elastic moduli of three-phase composites with the random inclusions
Faculty of Mechanical Engineering, Hanoi University of Industry, 298 Cau Dien Street, Bac Tu Liem District, Hanoi, Vietnam
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Accepted: 25 February 2022
Published online: 10 June 2022
In this work, some solutions such as Mori-Tanaka approximation (MTA), Differential approximations (DA), and Fast Fourier transformation method (FFT) were applied to estimate the elastic bulk and shear modulus of three-phase composites in 2D. In which two different sizes of circular inclusions are arranged randomly non-overlapping in a continuous matrix. The numerical solutions using FFT analysis were compared with DA, MTA, and Hashin-Strikman's bounds. The MTA and DA reasonably agreeable solution with the FFT solution shows the effectiveness of the approximation methods, which makes MTA, DA useful with simplicity and ease of application.
Key words: Elastic modulus / Fast Fourier transformation method (FFT) / Mori-Tanaka approximation / differential approximations / composite materials
© V.-L. Nguyen, published by EDP Sciences, 2022
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