Representative elementary volume via averaged scalar Minkowski functionals

TL;DR

This paper proposes a geometrical method using scalar Minkowski functionals to determine the Representative Elementary Volume (REV) in materials, showing that these functionals stabilize for sufficiently large sample sizes.

Contribution

It introduces a novel approach based on convex geometry and Minkowski functionals to evaluate REV, linking geometric properties to material heterogeneity.

Findings

Scalar Minkowski functionals stabilize for volumes larger than a threshold R^3.

Cubes of volume R^3 can serve as effective REVs based on functional stabilization.

The method provides a quantitative criterion for REV determination.

Abstract

Representative Elementary Volume (REV) at which the material properties do not vary with change in volume is an important quantity for making measurements or simulations which represent the whole. We discuss the geometrical method to evaluation of REV based on the quantities coming in the Steiner formula from convex geometry. For bodies in the three-space this formula gives us four scalar functionals known as scalar Minkowski functionals. We demonstrate on certain samples that the values of such averaged functionals almost stabilize for cells for which the length of edges are greater than certain threshold value R. Therefore, from this point of view, it is reasonable to consider cubes of volume R^3 as representative elementary volumes.