Fourier series expansion in non-orthogonal coordinate system for the homogenization of linear viscoelastic periodic composites

The Eshelby method and the Fourier series are used in order to determine the linear elastic and viscoelastic properties of composites with periodically distributed inclusions in a non-orthogonal coordinate system. The relaxation moduli provided by the proposed method are compared with the moduli obtained via FEM for a unidirectional composite. This comparison gives good results. The procedure results very useful for periodic composites with hexagonal symmetry, such as some transversely isotropic composites.