A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics

Abstract

AbstractThis work is directed to aleatoric and epistemic uncertainties in the framework of mean‐field and numerical homogenization, in order to determine the overall effective properties of transversely linear elastic fiber reinforced composite (FRC) which are taken into account by stochastic and fuzzy analysis. The stochastic part of material parameters is expanded with the multivariate polynomial chaos expansion, where for epistemic uncertainties the polynomial chaos coefficients are defined as design variables modeled as fuzzy sets. In this work, the combination of both types of uncertainty are treated with fuzzy‐random variables. Then, the fuzzy response for each selected α‐level is obtained from the minimum and maximum values of the quantity of interest (QoI). However, the QoI becomes a fuzzy‐random variable and depends on the design variables as well as the random variables. In order to avoid stochastic optimizations, so‐called surrogate QoIs are used, which can be described by ordinary and central moments. The representative example deals with a fuzzy‐random analysis of a unidirectional boron/aluminum FRC to demonstrate the versatility of the proposed formulation.