Homogenization of linear elastic properties of short-fiber reinforced composites - a comparison of mean field and voxel-based methods

The main contribution of this work lies in the detailed comparison of the predictions of linear elastic properties of mean field homogenization approaches and full field, voxel-based homogenization methods for short-fiber reinforced materials. In the former case, the self-consistent, the interaction direct derivative and a two-step-bounding approach, applying the Hashin-Shtrikman bounds, are used. In the latter case, the boundary value problem for representative volume elements is solved using fast Fourier transformation. Model microstructures with unidirectional aligned and two misaligned fiber configurations are considered exemplarily. Fiber volume fractions of 13%, 17% and 21% and phase contrasts of 44, 100 and 1000 in the elastic moduli have been taken into account. The different homogenization schemes are compared by means of effective directional dependent Young's modulus. This detailed comparison shows that mean field and full field solutions deliver similar results for moderate phase contrasts and volume fractions. Especially in the range of realistic phase contrasts like 44 for a composite of polypropylene and glass, the mean field approaches pose reliable alternatives for full field solution. Large phase contrasts result in relative deviations of up to 68%.