PSI - Issue 72

Stefan Hildebrand et al. / Procedia Structural Integrity 72 (2025) 520–528

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In future work, improvements regarding the amount of data and computational effort required for training will be investigated. Furthermore, the requirement of inner variables in the training data will be addressed by additional pre processing steps and an adapted NN architecture. The application of the presented procedure for other materials with kinematic hardening is straightforward, only the generation of appropriate surrogate data for training is necessary. Further quantities, e.g. the accumulated plastic strain, damage variables or separate quantities for tensile and compressive strain states can easily be introduced as additional input and output quantities of the NN, which extends the applicability of the procedure to a wide variety of materials. This will be demonstrated in a future work together with the generalizability of the approach for materials with non-associative flow including concrete Xenos and Grassl (2016). References Altenbach, H., Öchsner, A., editors, 2018, History of Plasticity. Springer Berlin Heidelberg, Berlin, Heidelberg, ISBN 978-3-662-53605-6. doi: 10.1007/978-3-662-53605-6_281-1. URL https://doi.org/10.1007/978-3-662-53605-6_281-1. As’ad, F., Avery, P., Farhat. C., 2022, A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12):2738–2759. doi: https://doi.org/10.1002/nme.6957. Umay Aydiner, I., Tatli, B., Yalçinkaya. T., 2024, Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174:103898, doi: https://doi.org/10.1016/j.ijplas.2024.103898. Aygün, S., Wiegold, T., Klinge., S., 2021, Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity, 143:103021, doi: https://doi.org/10.1016/j.ijplas.2021.103021. Baral, M., Ripley, P.W., Lou, Y., Korkolis. Y.P., 2024, Anisotropic ductile fracture of a stainless steel under biaxial loading: Experiments and predictions. International Journal of Plasticity, page 103927, doi: https://doi.org/10.1016/j.ijplas.2024.103927. Bland., D.R., 1957, The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1):71–78, doi: https://doi.org/10. 1016/0022-5096(57)90049-2. Bock, F.E., Aydin, R.C., Cyron, C.J., Huber, N., Kalidindi, S.R., Klusemann, B., 2019, A review of the application of machine learning and data mining approaches in continuum materials mechanics. Frontiers in Materials 6, doi: 10.3389/fmats.2019.00110. Bock, F.E., Keller, S., Huber, N., Klusemann, B., 2021, Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8), doi: 10.3390/ma14081883. Bonatti, C., Mohr. D., 2021, One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26): eabf3658, doi: 10.1126/sciadv.abf3658. Cazacu, O., Revil-Baudard, B., Chandola., N., 2019, Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials, volume 253 of Solid Mechanics and Its Applications. Springer, ISBN 978-3-319-92922-4. doi: https://doi.org/10.1007/978-3-319-92922-4. Dettmer, W., Reese., S., 2004, On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1):87–116, doi: https://doi.org/10.1016/j.cma.2003.09.005. Dornheim, J., Morand, L., Janarthanam Nallani, H., Helm, D., 2023, Neural networks for constitutive modeling – from universal function approximators to advanced models and the integration of physics Frederick, C.O., Armstrong, P.J., 2007, A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24:1 –26 Furukawa, T., Hoffman, M., 2004, Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3):195–204, doi: https://doi.org/10.1016/S0955-7997(03) 00050-X. Gorji, M.B,., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D., 2020, On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143:103972, doi: https://doi.org/10.1016/j.jmps.2020.103972. Hafiz, M.S., Hamad, ul H., Kuntz, M., Schäfer, J., Sonnweber-Ribic, J.P., Hartmaier, A., 2020, Inverse method to determine fatigue properties of materials by combining cyclic indentation and numerical simulation. Materials 13(14):3126, doi: doi:10.3390/ma13143126. Henkes,A., Wessels, H., Mahnken, R., 2022, Physics informed neural networks for continuum micromechanics. Computer Methods in Applied Mechanics and Engineering, 393:114790, doi: https://doi.org/10.1016/j.cma.2022.114790. Hildebrand, S., Klinge, S., 2024, Comparison of neural fem and neural operator methods for applications in solid mechanics. Neural Computing and Applications 7 2024a. doi: 10.1007/s00521-024-10132-2. Hildebrand, S., Klinge, S., 2024, Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with neural networks. Machine Learning: Science and Technology 5(4):045058, 12 2024b. doi: 10.1088/2632-2153/ad95da. Hornik, K., Stinchcombe, M., White, H., 1989, Multilayer feedforward networks are universal approximators. Neural Networks 2(5):359–366, doi: https://doi.org/10.1016/0893-6080(89)90020-8. Hu, Z., Jagtap, A.D., Karniadakis, G.E., Kawaguchi, K., 1976, Augmented physics-informed neural networks (apinns): A gating network-based soft domain decomposition methodology. Engineering Applications of Artificial Intelligence 126:107183, doi: https://doi.org/10.1016/j. engappai.2023.107183. Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P., 2020, A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365:113008, doi: https://doi.org/10.1016/j.cma.2020.113008. Jang, D.P., Fazily, P., Yoon, Y.W., 2021, Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138: 102919, doi: https://doi.org/10.1016/j.ijplas.2020.102919.