Applied Composite Materials 11: 33–55, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. 33 Effective Elastic and Plastic Properties of Interpenetrating Multiphase Composites XI-QIAO FENG ⋆ , ZHI TIAN, YING-HUA LIU and SHOU-WEN YU Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China e-mail: fengxq@tsinghua.edu.cn (Received 3 September 2003; accepted 18 September 2003) Abstract. In interpenetrating phase composites, there are at least two phases that are each in- terconnected in three dimensions, constructing a topologically continuous network throughout the microstructure. The dependence relation between the macroscopically effective properties and the microstructures of interpenetrating phase composites is investigated in this paper. The effective elastic moduli of such kind of composites cannot be calculated from conventional micromechanics methods based on Eshelby’s tensor because an interpenetrating phase cannot be extracted as dis- persed inclusions. Using the concept of connectivity, a micromechanical cell model is first presented to characterize the complex microstructure and stress transfer features and to estimate the effective elastic moduli of composites reinforced with either dispersed inclusions or interpenetrating networks. The Mori–Tanaka method and the iso-stress and iso-strain assumptions are adopted in an appropriate manner of combination by decomposing the unit cell into parallel and series sub-cells, rendering the calculation of effective moduli quite easy and accurate. This model is also used to determine the elastoplastic constitutive relation of interpenetrating phase composites. Several typical examples are given to illustrate the application of this method. The obtained analytical solutions for both effective elastic moduli and elastoplastic constitutive relations agree well with the finite element results and experimental data. Key words: micromechanics, constitutive relation, effective elastic moduli, interpenetrating phase composite, finite element analysis, Mori–Tanaka method, connectivity. 1. Introduction Recently, much attention has been attracted to interpenetrating or co-continuous phase composites, which contains at least two phases that are each interconnected in three dimensions, constructing a topologically continuous network throughout the microstructure. If any one of the constituent phases were removed from such a composite, the remaining material would form a self-supporting, open-celled foam which can still bear loading. Many biomaterials such as bones and trunks also have interpenetrating microstructures. Of late years, some methods (e.g., directed metal oxidation, self-propagating high-temperature synthesis, and gas pressure as- sisted infiltration) have been developed for synthesizing interpenetrating phase composites [1–12]. This new generation of composites possesses some physical ⋆ Corresponding author.