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.

通过微观图像分析，我们提出了一种确定代表性体积单元（RVE）大小的无需仿真的方法，该方法利用机器学习模型隐式表征输入微观图像的随机性质，并通过验证实验证明了我们选择的 RVE 大小与有限元仿真结果的一致性。