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A Fuzzy-Stochastic Multiscale Model for Fiber Composites: A one-dimensional study

We study mathematical and computational models for computing the deformation of fiber-reinforced cross-plied laminates due to external forces. This requires an understanding of both micro-structural effects and different sources of uncertainty in the problem. We first show that the uncertainties in the problem are of both statistical (aleatoric) and systematic (epistemic) types and that current multiscale stochastic models, such as stationary random fields, which are based on precise probability theory, are not capable of correctly characterizing uncertainty in fiber composites. Next, we motivate the applicability of models based on imprecise uncertainty theory and present a novel fuzzy-stochastic model, which can more accurately describe uncertainties in fiber composites. The new model is constructed by combining stochastic fields and fuzzy variables through a simple calibration-validation approach. Finally, we construct a global-local multiscale algorithm for efficiently computing output quantities of interest. The method aims at approximating required quantities, such as displacements and stresses, in regions of relatively small size, e.g. hot spots or zones. The algorithm uses the concept of representative volume elements and computes a global solution to construct a local approximation that captures the microscale features of the solution. The results are based on and backed by real experimental data.