A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures

TL;DR

This paper introduces a novel deep learning and pseudospectral polynomial chaos expansion based FFT homogenization algorithm for efficiently quantifying uncertainties in the effective properties of complex composite microstructures.

Contribution

It combines neural networks with pseudospectral polynomial chaos to create a fast surrogate model for uncertainty quantification in composite material homogenization.

Findings

The method accurately predicts moments of effective properties.

It is significantly faster than traditional homogenization approaches.

Demonstrated effectiveness on various microstructure examples.

Abstract

This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as well as in the fiber volume fraction. They are taken into account by multivariate random variables. Uncertainty quantification is achieved by an efficient surrogate model based on pseudospectral polynomial chaos expansion and artificial neural networks. An artificial neural network is trained on synthetic binary voxelized unit cells of composite materials with uncertain three dimensional microstructures, uncertain linear elastic material parameters and different loading directions. The prediction goals of the artificial neural network are the corresponding effective components of the elasticity tensor, where the labels for training are generated via a fast Fourier transform based numerical homogenization method. The trained artificial neural network is then used as a deterministic solver for a pseudospectral polynomial chaos expansion based surrogate model to achieve the corresponding statistics of the effective properties. Three numerical examples deal with the comparison of the presented method to the literature as well as the application to different microstructures. It is shown, that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches.