Characterization of Random Composite Properties Based on Statistical Volume Element Partitioning

Abstract

Homogenization of a representative volume element (RVE) is often used as the basis for defining the effective properties of a composite material. Although this is a powerful and useful approach for predicting global response, it does not capture the inherent variability of the material. Homogenization of statistical volume elements (SVEs), which are partitions of the RVE, provide a population of apparent properties that can be used to statistically characterize this local variability. The challenge to using these models lies in choosing a partitioning scheme and appropriate mesoscale to define the SVEs. In this work, two partitioning schemes are examined, a traditional square grid and polygon cells generated using Voronoi tessellation. Each scheme is used with a range of mesolength scales, i.e., partition sizes, and applied to composites with varied phase contrast ratios and differing microstructures. The resulting distributions of properties, described by probability density functions and generated using the principle of maximum entropy, are used to compare partitioning schemes. The results show consistent advantages to using Voronoi tessellation. This method reduces the impact of contrast ratio on property bounds, makes the choice of partition size less critical to a mesoscale model, and is able to better distinguish between subtle microstructural differences.