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Polynomial Chaos Characterization of Uncertainty in Multiscale Models and Behavior of Carbon Reinforced Composites



Design of non-crimp fabric composites (NCF) entails major challenges pertaining to (1) the complex fine-scale morphology of the constituents, (2) the manufacturingproduced inconsistency of this morphology spatially and across the layers, and thus (3) the ability to build reliable, robust, and efficient computational surrogate models to account for this complex nature. Traditional approaches to construct computational surrogate models have been to average over the fluctuations of the material properties up along the scale length. This fails to account for the fine-scale features and fluctuations in morphology, material properties of the constituents, as well as fine-scale phenomena such as damage and cracks. In addition, it fails to accurately predict the scatter in macroscopic properties, which is vital to the design process and behavior prediction. In this paper, we present an approach for addressing these challenges with minimum assumptions, by relying on polynomial chaos representations of both input parameters and material properties at different scales. Moreover, we emphasize the efficiency and robustness of integrating the polynomial chaos expansion with multiscale tools to perform multiscale assimilation, characterization, propagation, and prediction, all of which are necessary to construct the data-driven surrogate models required to design under the uncertainty of composites. These data-driven constructions provide an accurate map from parameters (and their uncertainties) at all scales and the system-level behavior relevant for design. While this perspective is quite general and applicable to all multiscale systems, NCF composites present a particular hierarchy of scales that permits the efficient implementation of these concepts.


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