PSI - Issue 72

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ScienceDirect

Procedia Structural Integrity 72 (2025) 520–528

12th Annual Conference of Society for Structural Integrity and Life (DIVK12) Physics-Informed Neural Network modeling of Cyclic Plasticity for steel alloy 4130 Stefan Hildebrand a, *, Sandra Klinge a a Technische Universität Berlin, Department of Structural and Computational Mechanics, Sekr. C8-3, Straße des 17. Juni 135, 10623 Berlin An efficient and explainable Machine Learning approach is presented replacing conventional material models based on the Radial Return Mapping algorithm for the constitutive modeling of cyclic plasticity. The presented model architecture is simpler and more efficient compared to existing solutions and needs approximately only half of NN parameters, while representing a complete three-dimensional material model. High accuracy and stability are achieved by physics-informed regularizations and including back stress information. The approach is validated by means of a case study for steel alloy 4130. The loss function is designed to stipulate several qualitative restrictions: deviatoric character of internal variables, compliance with the flow rule, the differentiation between elastic and plastic steps. The associativity of the flow rule, has only a minor impact on the accuracy, which implies the generalizability of the approach for a broad spectrum of materials undergoing plastic deformation. The validation shows cyclic stability and deviations in normal directions of less than 2% at peak values which is comparable to the order of measurement inaccuracies. © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia Abstract

Keywords: cyclic plasticity; constitutive modeling; machine learning; neural networks; NN; physics-informed

1. Introduction Machine learning methods have already been applied in a variety of ways to describe material behavior Bock et al. (2019); Dornheim et al. (2023); Rosenkranz et al. (2023). Goal of many applications is to replace analytical

* Corresponding author. Tel.:+00-000-000-000. E-mail address: stefan.hildebrand@tu-berlin.de

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 10.1016/j.prostr.2025.08.134