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 RYE 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 RYE as a weighted combination of specific realizations. These weighted combinations are referred to as RYE 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. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.