A study of the differential scheme for composite materials

The overall moduli of a 2-phase linearly elastic composite are estimated by the differential scheme. The phases may be arbitrarily anisotropic and 1 phase is regarded as similar ellipsoidal inclusions at any concentration embedded homogeneously in a matrix. For an isotropic dispersion of spheres and for a fibre reinforced material it is shown that the estimates of the overall moduli lie between their Hashin-Shtrikman bounds. Also some known exact results are reproduced using this scheme.