Quantification of Microstructure Induced Uncertainty in Multiscale Materials with Random Processes

Bostanabad, Ramin

doi:https://doi.org/10.21985/n2-5a6k-bc79

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Quantification of Microstructure Induced Uncertainty in Multiscale Materials with Random Processes

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The heart of computational materials science lies in providing fundamental insights and understanding of materials behavior and properties across different scales. The significance of this task is highlighted by the Materials Genome Initiative and the emergence of computational tools and frameworks such as materials by design, microstructure sensitive design, and integrated computational materials engineering. As a material’s microstructure heavily affects its properties, the central theme of these frameworks is to elucidate its relations to processing and properties. The goal of this dissertation is to develop frameworks and methods for computational microstructure quantification as well as statistical investigation of microstructure induced uncertainty on material properties. The overall contributions of this work are achieved in five research tasks and briefly discussed below. In predictive modeling of materials behavior as a function of their microstructure, it is highly desirable to quantitatively characterize the microstructure to achieve a deeper understanding on how the microstructure, on the one hand, is formed by composition and processing history and, on the other hand, affects the material properties. The characterized information, in turn, can be used to computationally reconstruct new microstructures to augment the available experimental data or even guide future experiments. Motivated by the timely need for a generic and efficient method for microstructure characterization and reconstruction (MCR), the contribution of my first research task is on developing a supervised learning-based approach for MCR that is applicable to a wide range of material systems and is accurate and computationally very efficient. Given the microstructure of a material system, high-fidelity computer simulations can be employed to predict the material properties. Such simulations have enabled the study of many fundamental phenomena but are generally expensive and hence not applicable to iterative materials design process. In addition, they discard correlated spatial microstructural variations (at the part-scale) and the associated uncertainties that inadvertently happen, e.g., in the manufacturing process. The goal of research tasks two through four is to build a unifying infrastructure to address these issues by quantifying the microstructure, modeling microstructural spatial variations via random fields (RFs), and replacing computer simulators with accurate but fast emulators. In task two, a novel method is developed that enables efficient and robust Gaussian process (GP) emulation by leveraging the smoothing effect of the nugget parameter on the likelihood profile. With this approach, more accurate GPs can be fitted to a wide range of datasets, i.e., high/low dimensions with/without noise. The developed method is used in later chapters for emulation as well as Bayesian analysis. In task three, a three-stage data-driven framework is developed for computational materials design that integrates feature-based MCR, design of experiments (stage one), high-fidelity computer simulations (stage two), statistical sensitivity analyses, and supervised learning (stage three). The contribution of this task is on developing a mechanistic data-driven approach to model complex microstructural behavior. In research task four, a two-stage approach is developed for uncertainty quantification (UQ) and propagation (UP) in multiscale simulations. The goal is to devise a non-intrusive UQ and UP approach that characterizes the uncertainties via RFs and is applicable to multiscale simulations where multiple uncertainty sources (including spatial microstructural variations) arise from different length-scales. In each chapter, the significance of the contributions is demonstrated via multiple examples. Predictions of a computer simulator in any scientific field are more reliable once the simulator is verified by and calibrated against some high-fidelity data. To this end, many works employ Bayesian statistics to make inferences about various aspects of a simulator by integrating the data and some prior knowledge. However, limited advancement has been done to enforce some physics-informed constraints such as positivity and monotonicity on the posterior distributions without significantly increasing the computation costs and complexities. The goal of research task five is to address these two challenges in the Bayesian analysis of multiscale computer simulators. In particular, a modular Bayesian calibration approach is developed that allows to take into account physical constraints and non-stationary noise variance. The developed approach is employed to calibrate and address the biases of a new constitutive law which is, subsequently, validated against independent experimental data in multiscale simulation of the preforming process (the most common large-scale production method for carbon fiber reinforced plastics).

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