The Voigt-Reuss (VR) and the Hashin-Shtrikman (HS) formulas are widely applied to estimate the upper and lower bounds of effective elastic properties of particulate composites, but they are not able to predict the specific values of the properties. The commonly used micromechanics models are inaccurate for composites that have large contrast of phase properties and high volume-fraction of inclusions. In this paper, we first demonstrate that the gap between the upper and the lower bounds is caused by the anisotropy existing in the micromechanics model. We then introduce a novel iterative isotropization procedure to remove the anisotropy and thus to eliminate the bound gap. Upon the convergence of the iteration procedure, the upper and the lower bounds become coincident, which provides a prediction of the property value. The validation and comparison against both experimental data and finite element modeling results show that, the new iterative formulas are able to predict the effective elastic properties more accurately than the commonly used micromechanics models, especially for particulate composites that have large contrast of phase properties and high volume-fraction of inclusions.