On the prediction of anisotropy in a binary composite due to the spacing among their fibers

Effective mechanical anisotropy in a fiber-reinforced composite material when both constituent phases have transversely isotropic mechanical properties is obtained by means of the asymptotic homogenization (AHM) and finite element (FEM) methods for the anti-plane longitudinal shear effective properties. It is shown that: (i) The source of anisotropy is the fiber spatial distribution in accordance with Neumann’s principle. (ii) Composite longitudinal shear properties, C1313C1313 and C2323C2323, obey the following statements: C1313(b/a)⩽C2323(b/a),C1313(b/a)=C2323(a/b)C1313(b/a)⩽C2323(b/a),C1313(b/a)=C2323(a/b) and C1313(a/b)=C2323(b/a)C1313(a/b)=C2323(b/a); where a>ba>b, being a and b the fiber spacing in the 1 and 2 directions.