Our goal is to devise a non-intrusive UQ and UP approach that characterizes the uncertainties via random fields (RFs) and is applicable to multiscale simulations where multiple uncertainty sources (including spatial microstructural variations) arising from different length-scales are coupled and spatially dependent. They are, however, seldom applied to multiscale simulations due to the significant computational costs and complexities. UQ and UP are actively pursued in various fields of science and engineering. For this reason, ever-growing research is being conducted to rigorously couple computational models with statistical uncertainty quantification (UQ) and uncertainty propagation (UP) methods to provide probabilistic predictions that are in line with the observed stochasticity in materials. Uncertainty is inevitably introduced in materials’ behaviors starting from the design and constituent selection stages, through the manufacturing processes, and finally during operation. Liu, Y., Greene, M.S., Chen, W., Dikin, D., Liu, W.K., “ Computational Microstructure Characterization and Reconstruction for Stochastic Multiscale Design”, Computer Aided Design, 45 (1), 65-76, 2013.C., and Chen, W., “ A Descriptor-based Design Methodology for Developing Heterogeneous Microstructural Materials System”, Journal of Mechanical Design, doi:10.1115/1.4026649, 2014. C., Apley, D., Wing K., and Chen, W., “ Computational Microstructure Characterization and Reconstruction: Review of the State-of-the-art Techniques”, Progress in Materials Science, 95, June 2018. Bostanabad, R., Zhang, Y., Li, X., Kearney, T., Brinson, L.Ghumman, U.F., Iyer, A., Dulal, R., Munshi, J., Wang, A., Chien, T., Balasubramanian, G., and Chen, W., “ A Spectral Density Function Approach for Active Layer Design of Organic Photovoltaic Cells”, Journal of Mechanical Design, Special Issue on Design of Engineered Materials and Structures, accepted July 2018.Li, X., Zhang, Y., Zhao, H., Burkhart, C., Brinson, L.C., Chen, W., “A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions”, Scientific Report, accepted 2018.Iyer, A., Zhang, Y., Dulal, R., Ghumman, U.F., Chien, T., Balasubramanian, G., and Chen, W., “ Designing Anisotropic Microstructures with Spectral Density Function”, Computational Materials Science, 179, 2020.“Nonstationarity Analysis of Materials Microstructures via Fisher Score Vectors”, Acta Materalia, 211,116818,2021. Our methods enable the integration of analyses and design decisions over multiple domains across manufacturing, structural mechanics, and design optimization.
For design of metamaterial systems, topology optimization and generative methods have been examined for designing multiscale and multifunctional structures. Advanced machine learning (e.g., Gaussian random process and deep learning), Bayesian inference, dimension reduction, and many more techniques are employed to address challenges such as high dimensionality, lack of data, big data, mixed-variable metamodeling and optimization. For design of heterogeneous microstructural systems, we develop statistical frameworks and tools that are tailored to a wide range of material systems. Built on the PSPP links, our research covers three major components of design methods for emerging materials, i.e., representation, evaluation, and synthesis.
The significance of this topic area is highlighted by the Materials Genome Initiative (MGI) and the integrated computational materials engineering (ICME) paradigm where the central theme is inverse materials design by elucidating the link between processing, structure, properties and performance (aka PSPP links). The heart of computational materials science and engineering lies in providing fundamental insights and understanding of materials behavior and properties across different scales, which further enables cost-effective design of materials with targeted properties.
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