A series–parallel mixture model to predict the overall property of particle reinforced composites

Motivated by stress and strain distributions in the unit cell obtained by the finite element analysis, a series–parallel mixture model is proposed to predict the overall property of particle reinforced composites. In this model, the matrix (softer) phase is split to two parts. The particle is first connected to one part in series, and then connected to the remaining part in parallel, eventually to form the composite. Numerical studies show that the in-series ratio is independent of material parameters and can be fitted as a function of particle volume fraction. The model is finally applied to predicting the overall property of composites with more than two phases and the relaxation of viscoelastic composites. The results validate the accuracy of the model.