The aim of the present work is to design and train 3D convolutional neural networks (3D-CNN) for linking arbitrary two-phase microstructures to their elastic macroscale stiffness thus replacing homogenization simulations. Since material samples are rarely periodic, periodic boundary conditions (PBC) are an approximation of what is  unknown. In order to account for this uncertainty, the CNNs are trained to provide for stiffness predictions an upper bound through kinematically uniform BCs (KUBC), and a lower bound through stress uniform BCs (SUBC). An inherent benefit is the information, whether the considered microdomain is large enough to be statistically representative, since in that case the microdomain is insensitive to the applied BCs [1]. We sketch the workflow of microstructure generation over the homogenization simulations based on an mpi-parallelized FE-HMM engine [2] up to the CNN architecture and training action. Tests demonstrate the predictive capacity of the CNNs, most notably for the real, two-phase microstructures of a diamond-based coating.  

References

[1] Huet, C. 1990, JMPS, 38(6), 813

[2] Eidel, B. & Fischer, A. 2019 CMAME, 329, 332