Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics

The concept of a representative volume element (RVE) is central to the establishment of robust microstructure–processing–property relationships in all hierarchical material systems. In this paper, we develop the main concepts underlying the rigorous definition of an RVE that reflects the complete set of 2-point statistics gathered from an ensemble of available microstructure data sets. In particular, it is shown that it is often impossible to identify a single realization of finite extent that meets this criterion. Instead, it is much more convenient to visualize the RVE as a weighted combination of specific realizations. These weighted combinations are referred to as RVE Sets in this work. This paper presents and validates a clear and precise definition of RVE Sets and their important role in efficiently capturing structure–property relationships in a number of material systems.