Two analytical models for the study of periodic fibrous elastic composite with different unit cells

In this work, the effective elastic moduli of two-phase fibrous periodic composites are obtained by means of the Asymptotic Homogenization Method (AHM) and eigenfunction expansion-variational method (EEVM), for different types of parallelogram cells. The constituents exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays of the cell related to the angle of the fibers is studied. Some numerical examples and comparisons with other theoretical results demonstrate that both methods (AHM and EEVM) are efficients for the analysis of composites with presence of rhombic cell. The effect of the configuration of the cells on the shear effective property is observed.