Statistical multiscale homogenization approach for analyzing polymer nanocomposites that include model inherent uncertainties of molecular dynamics simulations

A statistical multiscale homogenization strategy of polymer nanocomposites is proposed to account for the inherent uncertainties of molecular dynamics (MD) simulations. The proposed statistical multiscale homogenization scheme includes a discrete MD simulation system, a continuum theory of micromechanics of Eshelby's solution and two-scale homogenization, and Monte-Carlo simulations. The means and standard deviations of the elastic properties of the nanocomposites are quantified and discussed through statistical analyses that show the interphase effect. The elastic properties of the matrix, interphase, and composites are assumed to follow a lognormal distribution. An iterative inverse algorithm for obtaining the probability density distribution of the interphase is proposed and validated.