Multiscale Surrogate Modeling and Uncertainty Quantification for Periodic Composite Structures

Abstract

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.