Micromechanics of randomly oriented ellipsoidal inclusion composites. Part II: Elastic moduli

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Abstract
The elastic moduli of composites containing randomly oriented ellipsoidal inclusions are derived, calculated from the average stress and the average strain in the matrix and the inclusions, obtained using a modified Eshelby model. The quantitative expressions for the elastic moduli of the composite are obtained in relation to the volume fraction, the shape, and the elastic moduli of the inclusions. Specific cases are discussed: First, the elastic moduli of the materials containing randomly oriented penny‐shaped microcracks are derived and compared with those obtained by Budiansky and O’Connell [Int. J. Solids Struct. 12, 81 (1976)] and Nemat‐Nasser and Hori. The general expressions for the elastic moduli of multiphase inclusion composites and the effect of porosity or in the form of isolated voids on the elastic moduli of homogeneous materials and inclusion containing composites are derived. Experimental results have been employed to compare the predictions with engineering materials.

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