Probabilistic Prediction of Homogenized Property and Update of Prediction for Spherical Porous Material Considering Microstructural Uncertainties

Abstract

The purpose of this work is to simulate uncertainties existing in microscopic field of spherical porous material so that the homogenized property of interest can be predicted with high reliability. Moreover, the final goal is to build a bridge of feedback between microstructure design and fabrication to predict microstructure morphology by limited measurement data of macroscopic property. The uncertainties are identified as parametric variables in constituent material property and nonparametric variables in morphological fluctuation such as disordering and clustering in microstructure. First-order perturbation, based stochastic homogenization (FPSH) method together with mixture distribution technique is employed for probabilistic prediction. Furthermore, the update of prediction is accomplished in the case of an assumed virtual experimental trial. Two numerical examples show that the probabilistic prediction has given a better decision in microstructure design than deterministic prediction. The main conclusion coming from the new method derived by gap between measured data and prediction showed that, when the update is used for morphology prediction of microstructure, it is almost perfect agreement with parameters' setup of virtual experiment. After it is applied for update of probabilistic homogenized property, it could make the updated homogenized property closer to measurement data so that it becomes more realistic.