On the choice of homogenization method to achieve effective mechanical properties of composites reinforced by ellipsoidal and spherical particles

Abstract

In this paper, several rigorous numerical simulations were conducted to examine the relevance of mean-field micromechanical models compared to the Fast Fourier Transform full-field computation by considering spherical or ellipsoidal inclusions. To be more general, the numerical study was extended to a mixture of different kind of microstructures consisting of spheroidal shapes within the same RVE. Although the Fast Fourier Transform full field calculation is sensitive to high contrasts, calculation time, for a combination of complex microstructures, remains reasonable compared with those obtained with mean-field micromechanical models. Moreover, for low volume fractions of inclusions, the results of the mean-field approximations and those of the Fast Fourier Transform-based (FFTb) full-field computation are very close, whatever the inclusions morphology is. For RVEs consisting of ellipsoidal or a mixture of ellipsoidal and spherical inclusions, when the inclusions volume fraction becomes higher, one observes that Lielens' model and the FFTb fullfield computation give similar estimates. The accuracy of the computational methods depends on the shape of the inclusions' and their volume fraction.