Polynomial chaos expansion for uncertainty propagation analysis in numerical homogenization of 2D/3D periodic composite microstructures

Abstract

This paper proposes the use of adaptive polynomial chaos expansion (PCE) for uncertainty propagation analysis of the numerical homogenization of polymer composites doped with random dispersions of spherical inclusions. The developed PCE acts as a surrogate model bypassing the computationally intense numerical homogenization of the elastic properties of 2D/3D representative volume elements (RVEs) loaded with moderate to high filler contents. Numerical results and discussion are presented to assess the accuracy and computational efficiency of 2D and 3D homogenization meta-models. The ability of the developed approaches to perform uncertainty propagation analyses with minimum computational effort represents the main contribution of this work, which holds vast potential for the stochastic design of macroscopic composite structural elements.