The determination of the elastic properties of composite materials (multiphase aggregates, polycrystals, and porous or cracked solids) from the elastic properties of the components may be approached in several ways. The problem may be treated statistically, via scattering theory, through variational principles, or by the assumption of specific geometries for the material under consideration. Each of these methods is reviewed in turn. The widely used Voigt‐Reuss‐Hill average can be a poor approximation for both two‐phase composites and polycrystals, and its replacement by the two Hashin‐Shtrikman bounds is recommended. For pore‐containing or crack‐containing media, specific geometry models must be considered if useful results are to be obtained. If aggregate theory is used to estimate the moduli of individual components of a composite whose bulk properties are known, the shear moduli of the component phases must be matched (within a factor of 2 or 3) for the method to be useful. Results for nonlinear composites (which allow calculation of the pressure variation of aggregate moduli) have been obtained for only a few special cases.

Bounds on the effective elastic moduli of randomly oriented aggregates of hexagonal, trigonal, and tetragonal crystals are derived using the variational principles of Hashin and Shtrikman. The bounds are considerably narrower than the widely used Voigt and Reuss bounds. The Voigt-Reuss-Hill average lies within the Hashin-Shtrikman bounds in nearly all cases. Previous bounds of Peselnick and Meister are shown to be special cases of the present results.

Articles you may be interested inElastic properties of polycrystals with trigonal crystal and orthorhombic specimen symmetry J. Appl. Phys. 60, 3868 (1986); 10.1063/1.337558Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with trigonal (3,3) and tetragonal (4,4,4m) symmetry Bounds on the effective elastic moduli of randomly oriented aggregates of orthorhombic crystals have been derived using the variational principles of Hashin and Shtrikman. The bounds are considerably narrower than the widely used Voigt bound and Reuss bound. In many instances, the separation between the new bounds is comparable to, or less than, the uncertainty introduced by experimental errors in the single-crystal elastic stiffnesses. The Voigt-Reuss-Hill average lies within the Hashin-Shtrikman bounds.

Bounds on the effective elastic moduli of randomly oriented aggregates of monoclinic crystals are derived using the variational principles of Hashin and Shtrikman. The bounds are considerably narrower than the widely used Voigt and Reuss bounds. The Voigt-Reuss-Hill average lies within the Hashin-Shtrikman bounds in nearly all cases.