Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Tran, Anh; Robbe, Pieterjan; Rodgers, Theron; Lim, Hojun

doi:10.1007/s11837-023-06182-x

Title: Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Journal Article · Wed Oct 25 00:00:00 EDT 2023 · JOM. Journal of the Minerals, Metals & Materials Society

DOI:https://doi.org/10.1007/s11837-023-06182-x· OSTI ID:2320353

Tran, Anh ^[1]; Robbe, Pieterjan ^[2]; Rodgers, Theron ^[1]; Lim, Hojun ^[1]

Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Crystal plasticity finite element method (CPFEM) has been an integrated computational materials engineering (ICME) workhorse to study materials behaviors and structure-property relationships for the last few decades. These relations are mappings from the microstructure space to the materials properties space. Due to the stochastic and random nature of microstructures, there is always some uncertainty associated with materials properties, for example, in homogenized stress-strain curves. For critical applications with strong reliability needs, it is often desirable to quantify the microstructure-induced uncertainty in the context of structure-property relationships. However, this uncertainty quantification (UQ) problem often incurs a large computational cost because many statistically equivalent representative volume elements (SERVEs) are needed. In this article, we apply a multi-level Monte Carlo (MLMC) method to CPFEM to study the uncertainty in stress-strain curves, given an ensemble of SERVEs at multiple mesh resolutions. By using the information at coarse meshes, we show that it is possible to approximate the response at fine meshes with a much reduced computational cost. We focus on problems where the model output is multi-dimensional, which requires us to track multiple quantities of interest (QoIs) at the same time. In conclusion, our numerical results show that MLMC can accelerate UQ tasks around 2.23x, compared to the classical Monte Carlo (MC) method, which is widely known as ensemble average in the CPFEM literature.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)

Grant/Contract Number:: NA0003525

OSTI ID:: 2320353

Report Number(s):: SAND-2024-02799J

Journal Information:: JOM. Journal of the Minerals, Metals & Materials Society, Journal Name: JOM. Journal of the Minerals, Metals & Materials Society; ISSN 1047-4838

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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