Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters

Abstract This work is directed to polymorphic uncertain models in the framework of mean-field and full-field homogenization methods, in order to determine the effective properties of transversely linear elastic fiber reinforced composite (FRC). To this end, aleatoric and epistemic uncertainties are considered within a combined fuzzy random model. The random part is modeled by the multivariate polynomial chaos expansion, whereas the fuzzy part is modeled by fuzzy variables defined as fuzzy sets. The fuzzy response for each selected α -level is obtained from the minimum and maximum values of a quantity of interest (QoI). However, the QoI becomes a fuzzy random variable and depends on fuzzy variables as well as random variables. In order to avoid optimization of random variables, so-called surrogate QoIs are used, which are described by ordinary and central statistical moments. The representative examples deal with a fuzzy random analysis of a unidirectional FRC taken from the literature as well as a comparison with own experimental data for a carbon/epoxy resin FRC to demonstrate the versatility of the proposed formulation.

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