Deep Convolutional Neural Networks Predict Elasticity Tensors and their Bounds in Homogenization

TL;DR

This paper develops 3D convolutional neural networks to predict elastic stiffness and bounds of heterogeneous materials, replacing traditional homogenization simulations and enabling efficient analysis of microstructures.

Contribution

It introduces a CNN-based workflow that predicts elastic properties and bounds for various boundary conditions, improving efficiency and accuracy over explicit simulations.

Findings

CNN accurately predicts stiffness for synthetic and real microstructures.

The model provides bounds indicating proper RVE size.

Enables statistical analysis without costly simulations.

Abstract

In the present work, 3D convolutional neural networks (CNNs) are trained to link random heterogeneous, two-phase materials of arbitrary phase fractions to their elastic macroscale stiffness thus replacing explicit homogenization simulations. In order to reduce the uncertainty of the true stiffness of the synthetic composites due to unknown boundary conditions (BCs), the CNNs predict beyond the stiffness for periodic BC the upper bound through kinematically uniform BC, and the lower bound through stress uniform BC. This work describes the workflow of the homogenization-CNN, from microstructure generation over the CNN design, the operations of convolution, nonlinear activation and pooling as well as training and validation along with backpropagation up to performance measurements in tests. Therein the CNNs demonstrate the predictive accuracy not only for the standard test set but also for samples of the real, two-phase microstructure of a diamond-based coating. The CNN that covers all three boundary types is virtually as accurate as the separate treatment in three different nets. The CNNs of this contribution provide through stiffness bounds an indicator of the proper RVE size for individual snapshot samples. Moreover, they enable statistical analyses for the effective elastic stiffness on ensembles of synthetical microstructures without costly simulations.