On the behavior of elastic composites with transverse isotropic symmetry

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the effective elastic behavior of transversely isotropic composites made from two compressible elastic materials in prescribed proportions is examined. The set of all effective elasticity tensors for transversely isotropic finite rank laminar microstructures is described. The extremal property of this class of microstructures is used to derive new optimal bounds on the effective elastic moduli. For the special case of transversely isotropic fiber composites treated by Hashin we derive an optimal tensor inequality on the effective elastic tensor. The tensor inequality includes Hashin's and Hill's bounds on the transverse bulk modulus and Hashin's bounds on the transverse shear modulus and axial shear modulus. © 1991.

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Journal of the Mechanics and Physics of Solids

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