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Automated model discovery of finite strain elastoplasticity from uniaxial experiments

Asghar A. Jadoon, Knut A. Meyer, Jan N. Fuhg

TL;DR

The paper addresses learning constitutive laws for finite-strain elastoplasticity from uniaxial data. It develops a thermodynamically consistent framework by combining a finite-strain plasticity model with Physics Augmented Neural Networks (PANNs) to learn free-energy and dissipation potentials under convexity and monotonicity constraints. Through synthetic and experimental cyclic loading data, the authors show that the four-potential (4NN) configuration offers superior stress prediction and extrapolation, and that PANN-based models are more robust to initialization than traditional parameter-fitting. The approach reduces user bias, enforces physical laws by construction, and provides a systematic, physics-informed path toward automatic model discovery in history-dependent materials; future work includes sparsity-based interpretability and temperature/microstructure extensions.

Abstract

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical relationships were derived through experimentation and curve fitting. Recently, to automate the constitutive modeling process, data-driven approaches based on neural networks have been explored. While initial naive approaches violated established mechanical principles, recent efforts concentrate on designing neural network architectures that incorporate physics and mechanistic assumptions into machine-learning-based constitutive models. For history-dependent materials, these models have so far predominantly been restricted to small-strain formulations. In this work, we develop a finite strain plasticity formulation based on thermodynamic potentials to model mixed isotropic and kinematic hardening. We then leverage physics-augmented neural networks to automate the discovery of thermodynamically consistent constitutive models of finite strain elastoplasticity from uniaxial experiments. We apply the framework to both synthetic and experimental data, demonstrating its ability to capture complex material behavior under cyclic uniaxial loading. Furthermore, we show that the neural network enhanced model trains easier than traditional phenomenological models as it is less sensitive to varying initial seeds. our model's ability to generalize beyond the training set underscores its robustness and predictive power. By automating the discovery of hardening models, our approach eliminates user bias and ensures that the resulting constitutive model complies with thermodynamic principles, thus offering a more systematic and physics-informed framework.

Automated model discovery of finite strain elastoplasticity from uniaxial experiments

TL;DR

The paper addresses learning constitutive laws for finite-strain elastoplasticity from uniaxial data. It develops a thermodynamically consistent framework by combining a finite-strain plasticity model with Physics Augmented Neural Networks (PANNs) to learn free-energy and dissipation potentials under convexity and monotonicity constraints. Through synthetic and experimental cyclic loading data, the authors show that the four-potential (4NN) configuration offers superior stress prediction and extrapolation, and that PANN-based models are more robust to initialization than traditional parameter-fitting. The approach reduces user bias, enforces physical laws by construction, and provides a systematic, physics-informed path toward automatic model discovery in history-dependent materials; future work includes sparsity-based interpretability and temperature/microstructure extensions.

Abstract

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical relationships were derived through experimentation and curve fitting. Recently, to automate the constitutive modeling process, data-driven approaches based on neural networks have been explored. While initial naive approaches violated established mechanical principles, recent efforts concentrate on designing neural network architectures that incorporate physics and mechanistic assumptions into machine-learning-based constitutive models. For history-dependent materials, these models have so far predominantly been restricted to small-strain formulations. In this work, we develop a finite strain plasticity formulation based on thermodynamic potentials to model mixed isotropic and kinematic hardening. We then leverage physics-augmented neural networks to automate the discovery of thermodynamically consistent constitutive models of finite strain elastoplasticity from uniaxial experiments. We apply the framework to both synthetic and experimental data, demonstrating its ability to capture complex material behavior under cyclic uniaxial loading. Furthermore, we show that the neural network enhanced model trains easier than traditional phenomenological models as it is less sensitive to varying initial seeds. our model's ability to generalize beyond the training set underscores its robustness and predictive power. By automating the discovery of hardening models, our approach eliminates user bias and ensures that the resulting constitutive model complies with thermodynamic principles, thus offering a more systematic and physics-informed framework.
Paper Structure (9 sections, 43 equations, 14 figures, 4 tables)

This paper contains 9 sections, 43 equations, 14 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Finite strain plasticity formulation
  3. Standard model
  4. Finite strain plasticity with neural networks
  5. Results
  6. Synthetic Data
  7. Experimental Data
  8. Discussion
  9. Conclusions

Figures (14)

  • Figure 1: Simulation schematic for our analysis. The subscript $i$ represents the pseudo time step whereas subscript $n$ denotes the Newton-Raphson iteration for the evolution of internal variables which continues until a specified tolerance $tol$ is achieved for the residual.
  • Figure 2: Results for OW on the first synthetic dataset. (a) Evolution of the loss during the training routine for fitting the parameters to Ohno-Wang model for kinematic hardening. The lighter lines represent the loss evolution for different initialization whereas the darker line represents the mean loss. (b) True and predicted stress values from the best loss response.
  • Figure 3: Results for 2NN on the first synthetic dataset. (a) Evolution of the loss during the training routine for PANNs for dissipation potentials and fitting the parameters of Neo-Hookean free energies. The lighter lines represent the loss evolution for different initialization whereas the darker line represents the mean loss. (b) True and predicted stress values from the best loss response. (c) Model's performance on unseen data.
  • Figure 4: Results for 4NN on the first synthetic dataset. (a) Evolution of the loss during the training routine for PANNs for all the potentials. The lighter lines represent the loss evolution for different initialization whereas the darker line represents the mean loss. (b) True and predicted stress values from the best loss response. (c) Model's performance on unseen data.
  • Figure 5: Results for AF on the second synthetic dataset. (a) Evolution of the loss during the training routine for fitting the parameters to Armstrong-Frederick model for kinematic hardening. The lighter lines represent the loss evolution for different initialization whereas the darker line represents the mean loss. (b) True and predicted stress values from the best loss response.
  • ...and 9 more figures