EFFECTIVE ELASTIC-MODULI OF 2-PHASE COMPOSITES CONTAINING RANDOMLY DISPERSED SPHERICAL INHOMOGENEITIES

Based on the general micromechanical framework proposed in a companion paper, effective elastic moduli of two-phase composites containing ra ndomly dispersed spherical inhomogeneities are investigated in this pa per. At variance with existing micromechanical pairwise interaction mo dels (accurate up to the second-order in particle volume fraction phi) , the proposed approximate, probabilistic pairwise particle interactio n formulation coupled with the general ensemble-volume averaged field equations leads to a novel, higher-order (in phi), and accurate method for the prediction of effective elastic moduli of two-phase composite s containing randomly located spherical particles. The relevant ensemb le integrals in the proposed formulation are absolutely convergent due to a ''renormalization'' procedure employed in a companion paper. In accordance with the analogy between the effective shear modulus of an incompressible elastic composite with randomly dispersed rigid spheres and the effective shear viscosity of a colloidal dispersion with rand omly dispersed rigid spheres (at high shear rates), the proposed ensem ble-micromechanical approach is extended to predict effective shear vi scosities of colloidal dispersions at the high-shear limit. Comparison s with experimental data, classical variational bounds, improved three -point bounds, the second-order particle interaction model, and other micromechanical models are also presented. It is observed that signifi cant improvement in predictive capability for two-phase composites wit h randomly dispersed spheres can be achieved by using the proposed met hod.