Equation for elastic modulus of spherical inclusion composite
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The differential method is used to calculate the elastic moduli of a solid that contains a random distribution of spherical inclusions. Closed-form solutions are obtained for the two limiting cases of rigid inclusions and vacuous pores. These solutions obey the Hashin-Shtrikman bounds, and reduce to the correct values as the inclusion concentration approaches 0 or 1. The predictions are compared with data from the literature, and are shown to be very accurate over wide ranges of the inclusion concentration.
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