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Uncertainty quantification in multiscale simulation of woven fiber composites

机译：机织纤维复合材料多尺度模拟中的不确定度量化

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Woven fiber composites have been increasingly employed as light-weight materials in aerospace, construction, and transportation industries due to their superior properties. These materials possess a hierarchical structure that necessitates the use of multiscale simulations in their modeling. To account for the inherent uncertainty in materials, such simulations must be integrated with statistical uncertainty quantification (UQ) and propagation (UP) methods. However, limited advancement has been made in this regard due to the significant computational costs and complexities in modeling spatially correlated structural variations coupled at different scales. In this work, a non-intrusive approach is proposed for multiscale UQ and UP to address these limitations. We introduce the top-down sampling method that allows to model non-stationary and continuous (but not differentiable) spatial variations of uncertainty sources by creating nested random fields (RFs) where the hyperparameters of an ensemble of RFs is characterized by yet another RF. We employ multi-response Gaussian RFs in top-down sampling and leverage statistical techniques (such as metamodeling and dimensionality reduction) to address the considerable computational costs of multiscale simulations. We apply our approach to quantify the uncertainty in a cured woven composite due to spatial variations of yarn angle, fiber volume fraction, and fiber misalignment angle. Our results indicate that, even in linear analysis, the effect of uncertainty sources on the material's response could be significant. (C) 2018 Elsevier B.V. All rights reserved.
机译：机织纤维复合材料由于其优异的性能已越来越多地用作航空，建筑和运输行业的轻质材料。这些材料具有层次结构，因此必须在其建模中使用多尺度模拟。为了解决材料固有的不确定性，此类模拟必须与统计不确定性量化（UQ）和传播（UP）方法集成在一起。然而，由于在建模以不同比例耦合的空间相关的结构变化方面的大量计算成本和复杂性，在这方面仅取得了有限的进展。在这项工作中，针对多尺度UQ和UP提出了一种非侵入性方法，以解决这些限制。我们介绍了一种自上而下的采样方法，该方法允许通过创建嵌套的随机字段（RF）来对不确定性源的非平稳和连续（但不可区分）的空间变化进行建模，其中RF集合的超参数由另一个RF来表征。我们在自上而下的采样中采用了多响应高斯RF，并利用统计技术（例如元模型和降维）来解决多尺度模拟的可观计算成本。我们应用我们的方法来量化由于纱线角度，纤维体积分数和纤维未对准角度的空间变化而导致的固化机织复合材料的不确定性。我们的结果表明，即使在线性分析中，不确定性源对材料响应的影响也可能很大。 （C）2018 Elsevier B.V.保留所有权利。

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