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

  • Uncertainty Quantification and Design under Uncertainty for Metallic Systems
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Abstract

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. Our numerical results show that MLMC can accelerate UQ tasks around 2.23\(\times \), compared to the classical Monte Carlo (MC) method, which is widely known as ensemble average in the CPFEM literature.

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Acknowledgements

The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.

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  1. Sandia National Laboratories, Albuquerque, NM, 87123, USA

    Anh Tran, Theron Rodgers & Hojun Lim

  2. Sandia National Laboratories, Livermore, CA, 94550, USA

    Pieterjan Robbe

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  1. Anh Tran
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The authors thank two anonymous reviewers for their critics, which has substantially improved the quality of the manuscript. On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Tran, A., Robbe, P., Rodgers, T. et al. Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements. JOM (2023). https://doi.org/10.1007/s11837-023-06182-x

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