Bounds on the elastic and transport properties of two-component composites

Weshow in detail how the McCoy bounds on the effective shear modulus of a statistically isotropic composite, can be simplified and expressed in terms of the volume fraction, f₁, and two geometric parameters. ζ₁ and η₁. We simplify Silnutzer's bounds on the effective elastic moduli of fibre-reinforced composites and find they can be expressed in terms f₁and two geometric parameters, ζ'₁ and η'₁. The parameter ζ'₁ also determines bounds on the transport and optical constants of such composites. Also, the Elsayed-McCoy bounds on the transport properties of fibre-reinforced, symmetric-cell materials are shown to depend on three geometric parameters.