An effective inclusion model for effective moduli of heterogeneous materials with ellipsoidal inhomogeneities

In the present study, an effective inclusion model for effective elastic mo duli of heterogeneous materials is proposed to analyze the problem of an in finite matrix containing an ellipsoidal RVE. It is assumed that the strain energy changes of the infinite matrix due to embedding the RVE and its effe ctive inclusion into the matrix are identical. A system of equations for ef fective moduli is then formulated using the new energy balance equation tha t interrelate effective moduli to a problem of an infinite matrix containin g N inhomogeneities in an ellipsoidal sub-region. A generalized noninteract ing solution derived based on the present formulation coincides with the es timates of the Hashin-Shtrikman type obtained by Ponte Casta fi eda and Wil lis [J. Mech. Phys. Solids 43 (1995) 1919]. The effect of the shapes of RVE s on the approximate solution is also discussed in detail. As further appli cation of the present formulation, the numerical models for the effective m oduli of solids with cracks and heterogeneous materials with spherical inho mogeneities are proposed, which account for the interactions among many cra cks or spherical inhomogeneities. The numerical results are then compared w ith the existing micromechanics models and experimental data. (C) 2001 Else vier Science Ltd. All rights reserved.