Numerical Validation of Analytical Homogenization Models for the Case of Randomly Distributed and Oriented Ellipsoidal Fibers Reinforced Composites

The development of new composite materials can be a long and expensive process. It would therefore be relevant to have predictive tools that can predict the mechanical behavior of composites before their fabrication. Using these tools could lead to shorter certification time and cost reductions. Several analytical approaches exist for predicting the mechanical properties of composites. The best known are the Rule of Mixtures and the Classical Lamination Theory. In most cases, both approaches lead to inaccurate predictions since they do not take into account all the available information about the microstructure. Analytical homogenization models rely on microstructural information (e.g., constituents properties, volume fraction, shape, orientation, etc.) to predict the effective mechanical properties of heterogeneous materials. However, no systematic and thorough study evaluates the accuracy of these models for a wide range of constituents mechanical and geometrical properties. In order to validate the performance of analytical models, their predictions should be compared to those obtained by numerical methods. The different numerical methods that have been used in the literature had a high computational cost, which has limited the investigated range of composites. Furthermore, most numerical studies were performed without conducting a rigorous Representative Volume Element (RVE) determination process. The main purpose of this thesis was to validate the performance of analytical homogenization models at predicting the effective mechanical properties and local field statistics of randomly distributed and oriented ellipsoidal fibers reinforced composites. Since a large validation campaign was planned, a fully automated numerical tool was developed. The latter dealt with two independent steps: i)random generation of the representative microstructures and ii) accurate computation of the effective properties. The representative microstructures were generated using a molecular dynamics approach. A new computationally-efficient algorithm was developed for generating packings of randomly distributed and oriented ellipsoids. The proposed algorithm was able to generate all types of ellipsoids with high volume fractions and/or aspect ratios. The effective properties and local field statistics were accurately computed using a Fast Fourier Transforms (FFT) based technique. The predictions of the numerical tool were compared to those of the best known analytical homogenization models for a broad range of phases mechanical properties, fibers volume fractions and aspect ratios. The validation campaign involved a thorough and rigorous RVE determination process and approximately, 1800 different ellipsoidal fibers reinforced composites were studied. A validity domain was attributed to each analytical model. It was found that no analytical homogenization model stands out of the others as being more accurate over the studied range of phases mechanical and geometrical properties. However, if a single model was to be chosen to predict the effective properties and local field statistics of ellipsoidal fibers reinforced composites, this thesis recommend the Lielens' model.