Strain Gradient Modification of the Mori-Tanaka Model to Predict the Elastic Properties of the Layer by Layer (LBL) Polymer/Clay Nanocomposites

A size-dependent strain gradient Mori-Tanaka model (SGMT) is developed by applying strain gradient elasticity to the classical Mori-Tanka (M-T) method. The SGMT model is shown to be able to accurately predict the experimentally observed increase in stiffness of a layerby-layer (LBL)-assembled polyurethane-montmorillonite (PU-MTM) nanocomposite with various volume fractions. 3D Finite Element (FE) models of a representative volume element (RVE) are used to study the stiffness enhancement mechanism of the LBL PU-MTM nanocomposite. An effective constant thickness interphase is introduced in the FE simulations, which is analogous to using a formulation that incorporates strain gradient effects. An inverse method to determine the effective thickness and stiffness of the interphase layer using FE simulations is also presented.