Direct data-driven algorithms for multiscale mechanics

Creators: Prume, E.¹; Gierden, C.²; Ortiz, Michael³; Reese, S.^{1, 4}

1. RWTH Aachen University
2. Ruhr University Bochum
3. California Institute of Technology
4. University of Siegen

Abstract

We propose a randomized data-driven solver for multiscale mechanics problems which improves accuracy by escaping local minima and reducing dependency on metric parameters, while requiring minimal changes relative to non-randomized solvers. We additionally develop an adaptive data-generation scheme to enrich data sets in an effective manner. This enrichment is achieved by utilizing material tangent information and an error-weighted k-means clustering algorithm. The proposed algorithms are assessed by means of three-dimensional test cases with data from a representative volume element model.

Copyright and License

© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).

Acknowledgement

EP thanks Kevin Linka for very helpful discussions. EP, CG and SR gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG), Germany through the project “Multiscale modeling based on a novel combination of direct data-driven methods with Fourier transform-based microstructure simulation” (RE 1057/58-1, project number 532163998). MO gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060; project 441211072 - SPP 2256; and project 390685813 - GZ 2047/1 - HCM.

Funding

EP, CG and SR gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG), Germany through the project “Multiscale modeling based on a novel combination of direct data-driven methods with Fourier transform-based microstructure simulation” (RE 1057/58-1, project number 532163998). MO gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060; project 441211072 - SPP 2256; and project 390685813 - GZ 2047/1 - HCM.

Contributions

E. Prume: Writing – original draft, Visualization, Software, Methodology, Investigation, Data curation. C. Gierden: Writing – review & editing, Methodology. M. Ortiz: Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. S. Reese: Supervision, Project administration, Funding acquisition, Conceptualization.

Data Availability

Data will be made available on request.

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