Uncertainty propagation, entropy, and relative entropy in the homogenization of some particulate composites

Abstract

AbstractThe main idea of this work is an application of probabilistic entropy and also relative entropy in the numerical analysis of uncertainty propagation in the homogenization of some composite materials. The homogenization method is based on the determination of deformation energy for the representative volume elements computed with the use of some specific finite element method experiments. Uncertainty propagation concerns material and geometrical design parameters of particulate composites and is performed thanks to an application of polynomial responses; probabilistic moments of the effective tensor are computed via the iterative generalized stochastic perturbation technique and the semi‐analytical probabilistic method. Probabilistic entropy is determined according to Shannon theory, while relative entropies equations employed here follow mathematical models created by Kullback & Leibler, Jeffreys, Hellinger, and Bhattacharyya. Deterministic analyses have been performed with the use of the system ABAQUS, while all the remaining procedures have been programmed in the computer algebra system MAPLE.