Data-Efficient Machine Learning Approaches for Constitutive Modeling of Plasticity

  • Hildebrand, Stefan (Technische Universität Berlin)
  • Beerhues, Tonja (Technische Universität Berlin)
  • Klinge, Sandra (Technische Universität Berlin)

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Due to their versatility and efficiency in high-dimensional spaces, machine learning (ML) methods are increasingly adopted in a broad variety of engineering tasks in solid mechanics. In constitutive modeling, ML approaches facilitate inverse material characterization [1] and accelerate the characterization of new material types in highly automated lab environments [2] as well as materials design for highly special- ized applications as they occur e.g. in medical engineering [3]. Recent approaches target increasingly complex non-linear material behavior involving anisotropy and history-dependencies [4, 5]. This presentation provides an overview of recent developments in cyclic plasticity with a focus on hybrid data-driven and physics-informed training and outlines the path towards a unified framework for material characterization and simulation tasks. In particular, stateless recurrent neural network (RNN) architectures for the modeling of metal plasticity and concrete damage plasticity are presented. They replace classical evolution equations while retaining physical interpretability by explicitly incorporating internal variables, flow rules, and thermodynamic constraints through tailored loss functions and architectural design. It is shown, how physics-informed regularizations relieve the previous need for non-measurable quantities in the training data, such as backstress information, while simultaneously increasing the training and inference efficiency significantly. Further efficiency gains can be obtained by transfer learning based on models that have previously been trained for a material with comparable behavior. The validation demonstrates high accuracy, cyclic stability, and computational efficiency, underlining the readiness as drop-in replacements for conventional return-mapping algorithms. REFERENCES [1] Hildebrand S., Friedrich J.G., Mohammadkhah M., Klinge S., Coupled CANN-DEM simulation in solid mechanics, Machine Learning: Science and Technology, 6 (1), 015038, 2025. [2] Hildebrand S., Klinge S., Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with neural networks, Machine Learning: Science and Technology, 5 (4), 045058, 2024. [3] Graham M., Klinge S., Multiscale homogenisation of diffusion in enzymatically-calcified hydro- gels, Journal of the Mechanical Behavior of Biomedical Materials, 149, 106244, 2024. [4] Shoghi R., Hartmaier, A., A machine learning constitutive model for plasticity and strain har