Effective stiffness of composites reinforced by cylindrical fibers with smooth ends, with potential application to nanocomposites

Nanocomposite is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous random field of homogeneous cylindrical fibers with smooth ends and prescribed random orientation. Estimation of effective elastic moduli of nanocomposites was performed by the effective field method ( see for references Buryachenko in Appl Mech Rev 54: 1 - 47, 2001) developed in the framework of quasi crystalline approximation when the spatial correlations of inclusion location take particular ellipsoidal forms. A single cylindrical fiber with the smooth ends embedded in a large matrix sample is analyzed by finite element analysis for six different external loadings which yields a strain polarization tensor averaged over the volume of the fiber. The independent choice of shapes of inclusions and correlation holes provides the formulae of effective moduli which are symmetric, completely explicit and easy to use. The parametric numerical analysis reveals the most sensitive parameters influencing the effective moduli which are defined by the axial elastic moduli of nanofibers rather than their transversal moduli as well as by the choice of correlation holes, concentration and prescribed random orientation of nanofibers.