Uncertainty in effective elastic properties of particle filled polymers by the Monte-Carlo simulation

The main issue of this paper is to present statistical computational procedure for a determination of the effective elastic parameters for polymers filled with rubber particles. The homogenized elasticity tensor components are derived both as the variational upper and lower bounds as well as the solution for the cell problem on the composite Representative Volume Element. Probabilistic simulation is provided using both Monte-Carlo simulation technique and the generalized stochastic perturbation technique implemented in the symbolic computer algebra system MAPLE and, separately, together with the FEM-oriented code MCCEFF. Finally, up to fourth order probabilistic moments and coefficients of the homogenized tensor for the elastomers are computed as functions of the polymer's and particles' Young's moduli coefficients of variation. This study gives the basis for further homogenization-based experiments, where the hyperelastic constitutive model will replace the classical Hookean one applied here.