Probabilistic entropy and relative entropy for the effective characteristics of the fiber-reinforced composites with stochastic interface defects

Abstract

The main idea of this work is to investigate the uncertainty propagation while homogenizing the periodic fiber-reinforced composites with some structural interface imperfections, and specifically their thermal and mechanical properties in linear elastic regimes. The effective modules method is implemented here with the use of two alternative Finite Element Method (FEM) programs based on its displacement (temperature) formulation. Probabilistic (Shannon) entropy and probabilistic distance are engaged here to quantify uncertainty propagation of effective characteristics as well as their probabilistic distance to the original composite's characteristics. Probabilistic entropies fluctuations are contrasted with the traditional moments-based approach while increasing the input statistical scattering of material characteristics. According to the Maximum Entropy Principle Gaussian input parameters are tested as inducing the largest deviations in effective characteristics, but they are compared against some other symmetric distributions. The entire methodology is based upon the response random polynomials relating homogenized characteristics with material and geometrical parameters of the original composites subjected to randomization. Some series of the FEM experiments serve as the basis for the artificial neural network identification and optimization of these polynomials, whose application in conjunction with the Monte-Carlo simulation enables Shannon entropy determination. Relative entropy as well as the referential probabilistic moments are computed using the iterative generalized stochastic perturbation technique as well as the semi-analytical probabilistic method.