  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.
