  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.
