Simulation-Free Determination of Microstructure Representative Volume Element Size via Fisher Scores

TL;DR

This paper introduces a novel, simulation-free method to determine the RVE size of microstructures using Fisher scores, relying solely on micrograph analysis, thus saving computational resources in multiscale modeling.

Contribution

It proposes a new approach that estimates RVE size based on micrograph data and nonstationarity detection, eliminating the need for extensive FE simulations.

Findings

The method accurately identifies RVE sizes consistent with FE property convergence.

It reduces computational cost by avoiding multiple FE simulations.

The approach works for both simple and complex microstructures.

Abstract

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.