Numerical and analytical modeling of the stiffness of Polymer–Clay Nanocomposites with aligned particles: One- and two-step methods

This paper studies one- and two-step homogenization models for predicting the stiffness of Polymer–Clay Nanocomposites (PCN) with aligned particles. In particular, the influence of the Effective Particle (EP) concept central to two-step models is assessed for numerical as well as analytical modeling. This study covers intercalated PCN, as well as exfoliated morphologies in the presence of interphase. The predictions of analytical and simplified numerical homogenization models were compared against detailed 3D Finite Element (FE) simulations where the PCN layered microstructure is explicitly simulated. The Representative Volume Element (RVE) was rigorously determined. The theoretical predictions were also compared against experimental data extracted from the literature. It was found that both numerical and analytical two-step methods may significantly diverge from the FE simulations of the detailed microstructures. In general, the analytical multi-coated inclusions model delivers more reliable results than two-step methods. Despite their higher computational costs, one-step FE models are necessary, depending on the PCN microstructure and the desired accuracy. It was also found that the more the EP is different from the nanoclay, in terms of rigidity and aspect ratio, or the higher the volume fraction is, the more the accuracy of two-step numerical models is deteriorated.