Stationarity-constrained representative volume elements for image-based homogenization of granular microstructures

Abstract

We present an image-based workflow for representative elementary volume (REV) sizing in chemically mapped granular microstructures, applied to Arabian dune-sand samples characterized by mineralogical and textural heterogeneity. The REV is treated as a finite-window convergence scale within approximately stationary material domains, rather than as a global length assigned to a non-stationary image. Full-resolution backscattered-electron (BSE) gray-level maps are screened by local mean and standard-deviation compatibility to identify stationary domains. Candidate windows are sampled only inside these domains, and the representative support is selected using a persistent mean--spectral criterion requiring both the apparent-mean residual and the low-wavenumber covariance-spectrum residual to remain within tolerance over the non-reference tail. Ensemble reproducibility is used as an auxiliary check. Applied to seven full-resolution BSE images of dune-sand microstructures, the strict stationary-domain criterion gives $(L_{\rm REV}=1536~\mathrm{pixels})$, corresponding to $(\ell_{\rm REV}\approx2.01~\mathrm{mm})$ for a BSE pixel size of $(1.31~μ\mathrm{m})$. Property-level homogenization on QEMSCAN-derived numerical maps independently supports this millimetre-scale estimate: the converted support is $(L_{\rm REV}^{\rm prop}=201.2)$ pixels and is snapped to the nearest tested size, $(L_{\rm REV}^{\rm prop}=204)$ pixels $(\ell_{\rm REV}^{\rm prop}=2.04~\mathrm{mm})$. This length lies in the large-window regime of the apparent conductivity, stiffness, and directional Young-modulus curves. The workflow provides a reproducible route for REV sizing while making explicit its dependence on stationarity, image field, window sequence, and target observable.