  Computational modeling of the structural behavior of continuous fiber
composite materials often takes into account the periodicity of the underlying
micro-structure. A well established method dealing with the structural behavior
of periodic micro-structures is the so- called Asymptotic Expansion
Homogenization (AEH). By considering a periodic perturbation of the material
displacement, scale bridging functions, also referred to as elastic correctors,
can be derived in order to connect the strains at the level of the
macro-structure with micro- structural strains. For complicated inhomogeneous
micro-structures, the derivation of such functions is usually performed by the
numerical solution of a PDE problem - typically with the Finite Element Method.
Moreover, when dealing with uncertain micro-structural geometry and material
parameters, there is considerable uncertainty introduced in the actual stresses
experienced by the materials. Due to the high computational cost of computing
the elastic correctors, the choice of a pure Monte-Carlo approach for dealing
with the inevitable material and geometric uncertainties is clearly
computationally intractable. This problem is even more pronounced when the
effect of damage in the micro-scale is considered, where re-evaluation of the
micro-structural representative volume element is necessary for every occurring
damage. The novelty in this paper is that a non-intrusive surrogate modeling
approach is employed with the purpose of directly bridging the macro-scale
behavior of the structure with the material behavior in the micro-scale,
therefore reducing the number of costly evaluations of corrector functions,
allowing for future developments on the incorporation of fatigue or static
damage in the analysis of composite structural components.
