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A fuzzy-stochastic multiscale model for fiber composites A one-dimensional study

机译：复合材料的模糊随机多尺度模型一维研究

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We study mathematical and computational models for computing the deformation of fiber-reinforced polymers due to external forces. A thorough study requires an understanding of both micro-structural effects and uncertainty/variability in the manufacturing process, such as uncertainty in the size and distribution of fibers and variability in material properties and fracture parameters. We first show that the present uncertainties/variabilities, which are of both random and non-random types, cannot be accurately characterized by current stochastic multiscale models based on precise probability theory, such as stationary random fields. Next, we present a new hybrid fuzzy-stochastic model, which can more accurately describe uncertainties/variabilities in fiber composites. The new model, which is referred to as a fuzzy-stationary random field, consists of a random field with fuzzy moments. We then construct a global-local multiscale algorithm in a fuzzy-stochastic framework for efficiently computing output quantities of interest, such as displacements and stresses, in regions of relatively small size, e.g. hot spots. The algorithm utilizes the concept of representative volume elements and homogenization and constructs a global solution to compute a local approximation that captures the microscale features of the problem. The results are based on and backed by real experimental data through a calibration-validation approach. Published by Elsevier B.V.
机译：我们研究用于计算纤维增强聚合物由于外力而引起的变形的数学和计算模型。全面的研究需要了解制造过程中的微观结构效应和不确定性/可变性，例如纤维尺寸和分布的不确定性以及材料特性和断裂参数的可变性。我们首先表明，目前的不确定性/可变性既是随机类型又是非随机类型，不能通过基于精确概率理论的当前随机多尺度模型（例如平稳随机场）来准确表征。接下来，我们提出了一种新的混合模糊随机模型，该模型可以更准确地描述纤维复合材料中的不确定性/变异性。新模型称为模糊平稳随机场，由具有模糊矩的随机场组成。然后，我们在模糊随机框​​架中构造全局局部多尺度算法，以有效计算感兴趣的输出量（例如位移和应力）（例如相对较小的区域）。热点。该算法利用了具有代表性的体积元素和均质化的概念，并构建了一个全局解决方案来计算捕获问题的微观特征的局部逼近。结果基于真实的实验数据，并通过校准验证方法得到支持。由Elsevier B.V.发布

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