Elastic constants for an intercalated layered-silicate/polymer nanocomposite using the effective particle concept – A parametric study using numerical and analytical continuum approaches

The elastic constants are calculated for a layered-silicate/polymer nanocomposite with intercalated morphology using the effective particle concept. Two continuum approaches are employed and compared: a 2D numerical strategy using the finite element method (FEM) and Monte-Carlo simulation of the morphology, and an analytical approach based on the orientation averaged Mori-Tanaka method.The particular contribution of this paper is to study systematically the concept of the effective particle, as an aid to more efficient FEM modelling, or more accurate analytical modelling of elastic constants for layered-silicate nanocomposites, with different degrees of intercalation. In particular, it is shown that the concept is successful, provided that full anisotropy of the effective particle is acknowledged. It is also demonstrated that the effect of anisotropy is particularly pronounced, when transverse or shear response of the nanocomposite is considered, even for fully aligned reinforcement. If the effective particles become misaligned, this effect diminishes (for transverse and shear properties), especially for fully random orientations of particles. Finally, it is shown that the effect of anisotropy is also pronounced, when the gallery material is softer than the surrounding polymer.