Effective properties of fiber-reinforced materials: II—Bounds on the effective elastic moduli of dispersions of fully penetrable cylinders

Abstract

We evaluate third-order bounds on the effective transverse bulk and shear moduli of transversely isotropic fiber-reinforced materials for a distribution of fully penetrable cylinders in a matrix. The third-order bounds not only incorporate the simplest of statistical quantities, the fiber volume fraction φ 2, but also involve microstructural parameters which depend upon the threepoint matrix probability function of the model. The third-order bounds, for the fully penetrable-cylinder model and for a wide range of conditions, significantly improve upon second-order bounds on the effective transverse elastic moduli, due to Hill and to Hashin, which incorporate φ 2 only. In particular, when the fiber phase is as much as two orders of magnitude more rigid than the matrix phase, the Silnutzer bounds, for the model considered here, reduce the second-order bound widths by over 50% for 0 ≤ φ 2 ≤ 0.5.