Abstract:
The notion of “randomness” in the mathematical theory of composites has
typically been used abstractly within measure theory, making practical applications difficult.
In contrast, engineering sciences often discuss randomness too loosely, lacking a theoretical
foundation. This paper aims to bridge the gap between theory and applications, focusing on
the effective properties of two-dimensional conducting composites with non-overlapping
circular inclusions. It is shown that there is no universal minimum number of inclusions
per cell in simulations of random composites. Even minor changes to Random Sequential
Addition algorithms lead to different formulas for the effective constants. Application of the
analytical representative volume element (aRVE) theory methodologically and practically
addresses the diversity issue of random composites based on homogenization principles.
In particular, it examines how the spatial arrangement of inclusions impacts the overall
composite properties. The proposed method can be applied to a large number of inclusions
and to symbolically given geometric and physical parameters relevant to optimal design
problems. The method leverages structural sums and enables a more refined classification
of different classes of composites, which was unattainable using previous approaches. The
obtained results demonstrate a diversity of apparently similar composites. This paper
outlines the investigation strategy and provides a detailed description of each step.
