A Hierarchy-consistent Framework For SVE-based Multiscale Modeling Of Heterogeneous Materials
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We present a hierarchy-consistent multiscale framework for modeling the linear elastic response of two- phase heterogeneous materials. In multiscale analyses, Representative Volume Elements (RVEs) are commonly used to link microstructural features to macroscale behavior. Although effective in many settings, a single RVE realization often fails to capture the inherent variability of heterogeneous mi- crostructures. This limitation motivates the use of Statistical Volume Elements (SVEs), which provide a natural means of incorporating microstructural variability at an intermediate length scale. SVEs of increasing size are constructed by partitioning a large heterogeneous microstructure, and ap- parent elastic stiffness tensors are computed for each SVE. These homogenized SVEs are then used to assemble a block-based reconstructed macroscale model. A fully resolved direct numerical simulation (DNS) of the same heterogeneous microstructure serves as a macroscale reference solution. By subject- ing both the reconstructed model and the DNS to identical loading conditions, we directly evaluate the ability of SVE-based models to reproduce the macroscale response. We will analyze the effect of SVE size, in relation to other relevant length scales such as domain size, inclusion size, and a length scale that can be implied by loading, on the statistical variability of homoge- nized properties. Finally, we assess the computational efficiency and accuracy of multiple surrogate mod- eling strategies for SVE homogenization, including finite element–based SVE models, mean-field elastic homogenization, and machine learning (ML)-based surrogates trained on SVE response data. A direct comparison of DNS, FEM-SVE, mean-field, and ML-based models reveals the associated accuracy-cost trade-offs and identifies regimes where reduced-order and data-driven surrogates remain reliable. Over- all, this work provides a practical and systematic methodology for selecting appropriate SVE sizes and validating physics-based and data-driven surrogates in elastic multiscale simulations of two-phase mate- rials at the macroscale. REFERENCES [1] Abedi R., Garrard J., Acton K., Elastic and strength properties of statistical volume elements: Determination of isotropic and homogeneous size limits, Computers & structures, 277, 106959, 2023.
