Deep CNNs as universal predictors of elasticity tensors in homogenization
Bernhard Eidel
Abstract
In the present work, 3D convolutional neural networks (CNNs) are trained to link random heterogeneous, multiphase materials to their elastic macroscale stiffness thus replacing explicit homogenization simulations. The proposed CNN model is universal in that it accounts for various types of microstructures, for arbitrary phase fractions, non-constant and thereby very large ranges of Young’s moduli of the constituent phases (from 1 to 1000 GPa) and of their Poisson’s ratios (from 0 to 0.4). Moreover, the CNN predicts the stiffness for periodic boundary conditions (BCs) along with its upper bound through kinematically uniform BCs and its lower bound through stress uniform BCs. The triple of BCs reduces the stiffness uncertainty due to the embedding of the material volume into arbitrary adjacent host materials. Beyond, the stiffness bounds provide an indicator for the proper size of a representative volume element. The proposed universal CNN model achieves high accuracy in its predictions. The reasons for the rare outliers with larger errors are rigorously analyzed. For a real, two-phase diamond–SiC coating material the universal CNN is almost as accurate as a CNN exclusively trained for fixed elastic phase properties of that material. The speedup compared to finite element computations for homogenization is above factor 20 500. The proposed CNN model hence enables fast and accurate stiffness predictions in universal analyses of heterogeneous materials in their linear elastic regime.