Abstract
The classic tasks of computational engineers are to investigate and optimize structures in terms of their mechanical behavior. This iterative process usually requires a large number of calculations of different macroscopic structures of the same material. The computational time in this design-loop directly affects the time to market. Depending on the model complexity, describing the interaction between micro- and macro-scale can be computationally expensive and even prohibitive for engineering practice. This holds especially true if the physics on the micro-scale is complex involving inelastic behavior, fracture and/or phase change. In this paper, recent trends in Scientific Machine Learning (SciML), which may advance computational homogenization in the sense of the digital twin paradigm, are reviewed. We believe that SciML techniques for computational homogenization will make micro-macro simulations become applicable at low extra cost in engineering practice. This work is partially funded by the DFG Priority Program SPP 2020 Experimental-Virtual-Lab and the DFG Collaborative Research Center SFB 1153 Tailored Forming.
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Acknowledgements
FA, MH, MH, LL and PW acknowledge funding through the DFG Priority Program SPP 2020 Experimental-Virtual-Lab under the grants number 373757395; project WR 19/58-2 and GZ-LO 751/22-2 (668132). CB, FA and PW thank the German Research Foundation (DFG) for financial support to this work in the Collaborative Research Center SFB 1153 Process chain for the production of hybrid high-performance components through tailored forming with the subproject C04 Modelling and simulation of the joining zone, project number 252662854.
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Wessels, H. et al. (2022). Computational Homogenization Using Convolutional Neural Networks. In: Aldakheel, F., Hudobivnik, B., Soleimani, M., Wessels, H., Weißenfels, C., Marino, M. (eds) Current Trends and Open Problems in Computational Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-87312-7_55
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