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Homogenized mechanical properties: from direct numerical simulation over reduced order modeling to data-driven surrogate models.

The simulation of microstructured materials is an important field in computational materials science and in industrial settings. The exploration of potential material designs using in silico predictions is continuously gaining significance. In this talk different approaches for solving computationally challenging homogenization problems are addressed. Starting from 3D image data, voxel discretizations in combination with regular trilinear finite elements are used in combination with FFT-based preconditioning in our solver FANS. Such direct numerical methods are interesting if a limited number of load cases is considered. However, when dealing with nonlinear problems and in many query settings (e.g. in twoscale simulations) the use of reduced order models (ROM) will be described as a solid compromise of accuracy and performance. Machine learned surrogate models can outperform ROM, but they have a limited validity domain and they are not applicable in path-dependent problems without trickery. The presentation will close with an overview of the strengths and weaknesses of the different methods.