Mathematical and finite element analysis estimations of the reinforcement effect on Young's modulus of polymer membrane/montmorillonite clay nanocomposites

This work attempts to estimate the effect of the reinforcement percentage on Young's modulus for membranes of polymer‐clay nanocomposites (PCNs). Models tried to simulate different contents of the reinforcement for experimentally obtained PCNs with nanometric montmorillonite clays (MMT) incorporated into a polynorbornene dicarboximide matrix. The analyses were carried out modeling through discrete element method (DEM) and finite element analysis (FEA) volume fractions from 0.01 to 0.025 of elliptical MMT nano‐platelets with aspect ratios = 0.2 (1000 × 500 nm) and thicknesses of 1 nm. These models were generated using as starting point the morphology and distribution of the reinforcements observed in scanning electron microscopy for experimental PCNs. Estimations were compared to predictions obtained by Rule of Mixtures and other mathematical models. Results showed that the elastic modulus of the nanocomposites significantly rises as MMT volume fraction increases. Besides, the use of DEM‐FEA generated the predictions closest to the experimental values, with relative errors lower than 10%. For the other models, the errors were significantly high, even reaching 100%. This shows the importance of DEM‐FEA to obtain a more accurate model of a real composite and a better estimation of its mechanical behavior.