This paper presents an analytical determination of the elastic constants of composite materials with transversely isotropic elastic circular fiber inclusions in terms of the elastic moduli and the geometric parameters of the constituents. Hexagonal array fiber arrangement is assumed. The problem is solved within the framework of linear elasticity theories of isotropic and anisotropic elastic bodies by subjecting the composite to uniform normal and shearing strain fields. Solutions are obtained in series forms and the Fourier method and the least-square method are used. Numerical results are compared with existing analysis and experiments.

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