Effective field methods vs finite element models for microgeometries with ellipsoidal inclusions. Theory and application

Abstract

This study compares the predictions of analytical and numerical models employing ellipsoidal inclusions to determine the effective properties of composite materials. Three groups of factors influencing homogenization accuracy are investigated: the type of homogenization problem (elasticity, expansion, and conductivity), the material phase characteristics (isotropy, inclusion orientation, and inclusion aspect ratio), and the modeling methodologies, where effective field methods (EFMs) – including the Non-Interaction, the Mori–Tanaka and Maxwell methods – are evaluated against the pseudo grain decomposition method (PGDM) and numerical finite element (FE) models in a parametric study. The study considers ellipsoidal inclusions with aspect ratios ranging from 0.2 to 5 and orientation scattering from completely random to fully aligned. The results indicate that the type of homogenization problem does not significantly affect the prediction accuracy of EFMs and that the Mori–Tanaka and Maxwell methods show excellent agreement with FE models for all properties. The PGDM is shown to yield reliable results only for certain elastic properties (e.g., $E_{11}$) for composites with inclusions of aspect ratios greater than 1. Therefore, it is concluded that the Mori–Tanaka and the Maxwell methods serve as the most suitable analytical alternatives to computationally intensive FE models.