Towards deep learned constitutive models based on two‐dimensional strain fields. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Hillgärtner, Markus; Linka, Kevin; Abdolazizi, Kian P.; Itskov, Mikhail
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900159
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In order to calibrate material models, experimental stress‐strain curves are usually compared with model predictions under the same loading conditions. While this approach guarantees good results for one specific loading type, the resulting model is not generally able to properly predict other loading scenarios. Therefore, a variety of mechanical tests can be conducted, amongst which uniaxial tension, uniaxial compression, pure‐shear and equibiaxial tension tests are the most commonly used ones. Multi‐axial loading often cannot be adequately predicted solely based on test data from one such experiment. Therefore, the material model can be fitted against several mechanical test data sets simultaneously in order to increase the prediction quality, which requires a considerable amount of experiment work. This contribution aims to create phenomenological material models which are directly fitted against an experimental force response and the corresponding two‐dimensional strain field obtained from arbitrary loading. To this end, a deep learning framework based on a multilayer‐perceptron (MLP) approach [2] is proposed which identifies suitable strain‐energy functions and their corresponding derivatives. These can be utilized in a commercial finite element code via a user defined material subroutine in order to compare the quality of the approximation with the reference data. This approach avoids the above mentioned idealized experiments and simplifies the process of phenomenological modeling by exploiting the capabilities of deep neural networks.