Effective moduli of nanoparticle reinforced composites considering interphase effect by extended double-inclusion model – Theory and explicit expressions

In this work, an extended double-inclusion model incorporating finite matrix volume fraction is derived by the method of Eshelby’s equivalent inclusion and Mori–Tanaka’s average theory, which can be used to predict overall mechanical properties of nanocomposites considering particle/matrix interphase effects. For convenience of engineering applications, the explicit expressions of the effective elastic moduli for composites with distributions of unidirectionally aligned, three- and two-dimension randomly oriented spheroidal particles, respectively, are obtained. The results can be used to predict effective properties of nanocomposites including interphase effects.