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 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.