Homogenization models for predicting local field statistics in ellipsoidal particles reinforced composites: Comparisons and validations

Abstract

This paper validates the performance of analytical homogenization models at predicting the local field statistics in randomly distributed and oriented ellipsoidal particles reinforced composites. The numerical validation was based on a newly introduced load independent metric, which allowed to formulate general conclusions. A large validation campaign was conducted and the Representative Volume Element (RVE) was rigorously determined for each combination of phases mechanical properties, particles volume fraction and aspect ratio. The load independent properties computed numerically were compared to those predicted by a range of analytical models. The study revealed that the original Benveniste’s interpretation of the Mori–Tanaka scheme led to the most accurate first order moments and intra-matrix second order moments, provided that the mechanical properties contrast between the particles and the matrix are low. For higher contrasts, Lielens’ model delivers the most accurate estimates. The self-consistent scheme is the most suited model to predict the intra-particle second order moments when the particles aspect ratio is low. For particles with high aspect ratio, Lielens’ model could be an alternative to the self-consistent scheme. Furthermore, an interpolation model has been developed and it has been shown to predict accurately the mean and covariance tensors of the intraphase stress fields.