Multiscale study on determining representative volume elements size for mechanical behaviours of complex polymer nanocomposites with nanoparticulate agglomerations

Representative volume elements (RVE) have been widely employed to describe and predict the various effective properties of heterogeneous composite systems. In this present study with an interphase property degradation model, a multiscale analysis is performed to investigate the mechanical behaviours of polymer nanocomposites containing nanoparticulate agglomerations. Using the Fourier transform approach on the structural property variation at given cell lengths, the smallest RVE size (the minimum allowable length for an approximate description of the material system) is determined based on the coefficient of variation. It is reasonable to select an RVE size that is equal to a quarter of the most dominant wavelength as the minimum RVE size. A novel user-defined factor-based approach similar to the concept of margin of error is proposed to determine the optimal sampling number at a specific RVE size. The precision approach can provide accurate estimation of the mechanical properties of the nanocomposites with reduced computational cost.