On the rule of mixtures for predicting the mechanical properties of composites with homogeneously distributed soft and hard particles

The concept of the mixtures can be used not only in composites but also in materials with precipitates and matrix. In this investigation, a finite element method of axisymmetric unit cell model and the rule of mixtures of Voigt model and Reuss model are used to analyze the overall mechanical response of composites with homogeneously distributed particles. The calculations have been carried out by taking the materials as a hardening material and a perfectly plastic material. The elastic and plastic properties are predicted for various volume fractions of the soft and hard particles. The computational results are compared with the results of the rule of mixtures. It is found that the plastic flow curves agree well with the Voigt model for a high volume fraction of the particles and exist within the Voigt model and the Reuss model for a low volume fraction of the particles.