mlsanityData to 14 Oct 2026

Modular machine learning-based elastoplasticity: generalization in the context of limited data

arXiv 2210.08343 ↗First posted 15 Oct 2022cs.LG cs.CEcited by 16

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Abstract (arXiv)

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish stress-evolution laws that avoid user-chosen functional forms by relying on machine learning representations and algorithms. However, these approaches not only require a significant amount of data but also need data that probes the full stress space with a variety of complex loading paths. Furthermore, they rarely enforce all necessary thermodynamic principles as hard constraints. Hence, they are in particular not suitable for low-data or limited-data regimes, where the first arises from the cost of obtaining the data and the latter from the experimental limitations of obtaining labeled data, which is commonly the case in engineering applications. In this work, we discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information and the complexity of the response. The method is tested on synthetic uniaxial data coming from simulations as well as cyclic experimental data for structural materials. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data. Training aspects and details of the implementation of these models into Finite Element simulations are discussed and analyzed.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 20 of its 101 references that are in the map. First posted on arXiv 15 Oct 2022.

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20 of 101 references.

References · 20

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8 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 5; 2024: 3; 2025: 3; 2026: 5.

16 papers.

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  1. 2024A review on data-driven constitutive laws for solidscited by 35
  2. 2023Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanicscited by 16
  3. 2023Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressionscited by 10
  4. 2023Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksencited by 9
  5. 2023Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINNcited by 6
  6. 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
  7. 2024Improving the performance of Stein variational inference through extreme sparsification of physically-constrained neural network modelscited by 4
  8. 2026Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)cited by 3
  9. 2025Input Specific Neural Networkscited by 2
  10. 2023A machine learning-based viscoelastic-viscoplastic model for epoxy nanocomposites with moisture contentcited by 1
  11. 2025Physics-based machine learning for fatigue lifetime prediction under non-uniform loading scenarioscited by 0
  12. 2025Hybrid twinning using PBDW and DeepONet for the effective state estimation and prediction on partially known systemscited by 0
4 more
  1. 2026Physics-Informed Gaussian Process Regression for the Constitutive Modeling of Concrete: A Data-Driven Improvement to Phenomenological Modelscited by 0
  2. 2026Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representationscited by 0
  3. 2026A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modelingcited by 0
  4. 2026Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modelingcited by 0