  A representative volume element (RVE) is a reasonably small unit of
microstructure that can be simulated to obtain the same effective properties as
the entire microstructure sample. Finite element (FE) simulation of RVEs, as
opposed to much larger samples, saves computational expense, especially in
multiscale modeling. Therefore, it is desirable to have a framework that
determines RVE size prior to FE simulations. Existing methods select the RVE
size based on when the FE-simulated properties of samples of increasing size
converge with insignificant statistical variations, with the drawback that many
samples must be simulated. We propose a simulation-free alternative that
determines RVE size based only on a micrograph. The approach utilizes a machine
learning model trained to implicitly characterize the stochastic nature of the
input micrograph. The underlying rationale is to view RVE size as the smallest
moving window size for which the stochastic nature of the microstructure within
the window is stationary as the window moves across a large micrograph. For
this purpose, we adapt a recently developed Fisher score-based framework for
microstructure nonstationarity monitoring. Because the resulting RVE size is
based solely on the micrograph and does not involve any FE simulation of
specific properties, it constitutes an RVE for any property of interest that
solely depends on the microstructure characteristics. Through numerical
experiments of simple and complex microstructures, we validate our approach and
show that our selected RVE sizes are consistent with when the chosen
FE-simulated properties converge.
