Article introduces the Fast-Fourier transformation method (FFT) and an approximation method to calculate the conductivity of compound-inclusion composites in two-dimensional space. The approximation compares favorably with the numerical results for a number of periodic and random models over a range of volume proportions of phases, but divers at large volume proportions of the included phases when the interactions between the inclusions are more pronounced. | Vietnam Journal of Mechanics, VAST, Vol. 37, No. 3 (2015), pp. 169 – 176 DOI: FFT SIMULATIONS AND MULTI-COATED INCLUSION MODEL FOR MACROSCOPIC CONDUCTIVITY OF 2D SUSPENSIONS OF COMPOUND INCLUSIONS Nguyen Van Luat1 , Nguyen Trung Kien2,∗ 1 Hanoi University of Industry, Vietnam 2 University of Transport and Communication, Hanoi, Vietnam ∗ E-mail: ntkien@ Received October 22, 2014 Abstract. Article introduces the Fast-Fourier transformation method (FFT) and an approximation method to calculate the conductivity of compound-inclusion composites in two-dimensional space. The approximation compares favorably with the numerical results for a number of periodic and random models over a range of volume proportions of phases, but divers at large volume proportions of the included phases when the interactions between the inclusions are more pronounced. Keywords: Effective conductivity, Fast Fourier methods, matrix composite, coated-inclusion. 1. INTRODUCTION Theoretical determination the effective conductivity of heterogeneous materials is usually complicated due to the complexity of the microstructure and limited information about the composites, such as the properties and volume proportions of the component materials. An approach to the problem is to construct upper and lower bounds based on the variational formulations [1, 2]. Matrix-particulate composite are suspensions of particle-inclusions in a continuous materials. In many cases the inclusions have the structure that can be presented as multi-coated inclusions. A simplest 2D model for such composites are multi-coated circle assemblage model, when the matrix phase is described as the outermost circular cell - an extension of Hashin-Shtrikman two-phase circle assemblage. More accurate estimations in particular cases would require more detailed numerical simulations. In this work we apply both numerical FFT method and the simple multi-coated circle assemblage approximation to .
