In this paper, the mechanical behavior of composite materials with periodic microstructure is analysed. The corresponding elastic problem is solved by using the Fourier series technique and assuming the homogenization eigenstrain to be piecewise constant. Then, the coefficients of the overall stiffness tensor of the composite material are expressed analytically in terms of the elastic properties of the constituents (fibers and matrix) and as a function of nine triple series which take into account the geometry of the inclusions. In the case of composite materials reinforced by long fibers, simple formulas for evaluating these series are proposed. Close-form expressions for the elastic moduli of the fiber reinforced composite with periodic microstructure and for the equivalent transversely isotropic material are obtained. Finally, several comparisons with experimental results are presented. © 1994.
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