Probabilistic Relative Entropy in Homogenization of Fibrous Metal Matrix Composites (MMCs)

Abstract

The main aim of this work is to deliver uncertainty propagation analysis for the homogenization process of fibrous metal matrix composites (MMCs). The homogenization method applied here is based on the comparison of the deformation energy of the Representative Volume Element (RVE) for the original and for the homogenized material. This part is completed with the use of the Finite Element Method (FEM) plane strain analysis delivered in the ABAQUS system. The probabilistic goal is achieved by using the response function method, where computer recovery with a few FEM tests enables approximations of polynomial bases for the RVE displacements, and further—algebraic determination of all necessary uncertainty measures. Expected values, standard deviations, and relative entropies are derived in the symbolic algebra system MAPLE; a few different entropy models have been also contrasted including the most popular Kullback–Leibler measure. These characteristics are used to discuss the influence of the uncertainty propagation in the MMCs’ effective material tensor components, but may serve in the reliability assessment by quantification of the distance between extreme responses and the corresponding admissible values.