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 φ2, 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 φ2 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 ≤ φ2 ≤ 0.5.
All Science Journal Classification (ASJC) codes
- General Materials Science
- General Engineering
- Mechanics of Materials
- Mechanical Engineering