An iterative Mori–Tanaka approach

Abstract

The aim of this paper is to evaluate the effective material properties of particle-reinforced composites. The Mori–Tanaka approach overstates the strain of inclusions and therefore underestimates the resulting effective rigidity of composite materials. We propose an iteration method for the Mori–Tanaka approach. Initially, the effective elastic tensor of a composite material is found by using the Mori–Tanaka approach. Then the new composite is taken as a background material, and the inclusions and matrix are both embedded into it. The resulting material is softer than predicted by the self-consistent approach, but stiffer than forecasted by the Mori–Tanaka method. The predictions are compared with data from the literature and are shown to be very accurate over wide ranges of inclusion concentration.