On the effective moduli of composite materials: Slender rigid inclusions at dilute concentrations

Abstract

Using slender-body theory the effective elastic moduli of a certain class of composite materials are determined by analyzing the response of an infinite elastic medium, containing a single slender rigid inclusion, to a given applied strain. Solutions are found as perturbation expansions in the slenderness ratio of the inclusion, κ, which is small. These then yield the five independent elastic moduli, which characterize the macroscopic state of a dilute dispersion of slender rigid inclusions aligned in a common direction. The increase in rigidity due to the inclusions is found to be of order φ/κ2 ln(2/κ) for the longitudinal Young's modulus and of order π for the other four moduli, where π is the volume fraction of inclusions. Although the general theory is restricted to axisymmetric inclusions having ends which are no more blunt than a prolate spheroid, the results are shown to be valid approximations for circular cylinders in certain cases. © 1972 Birkhäuser Verlag.