Comparison of micromechanics methods for effective properties of multiphase viscoelastic composites

In this paper we examine the use of several popular micromechanics methods for determination of effective composite properties when all phases are viscoelastic. The elasticity-based Mori-Tanaka method and the finite element method of cells are used, both via implementation of the elastic-viscoelastic correspondence principle. The finite element technique considers two different periodic microstructures, square and hexagonal arrays, the results of which are compared with each other and the Mori-Tanaka predictions. The resultant effective properties for viscoelastic composites are determined at a wide range of frequencies and compared with transformed Hashin-Shtrikman bounds and Gibiansky-Milton bounds. The Mori-Tanaka method in the transformed domain is by far the simplest to implement and it is shown that the method replicates the major features of the storage and loss moduli of the composite, including location and magnitude of the double loss peaks from the glass-rubber transition of each phase. It is also illustrated that the Mori-Tanaka method predicts a nearly log-linear relationship between resultant property and volume fraction at a given frequency. Limitations of the Mori-Tanaka method for viscoelastic composites are highlighted. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.