# Discovering plasticity models without stress data

arXiv: https://arxiv.org/abs/2202.04916 · HTML: https://mlsanity.com/paper/2202.04916/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2022.

## Built on by (most cited first, 28 of 28)

- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Modular machine learning-based elastoplasticity: generalization in the context of limited data](https://mlsanity.com/paper/2210.08343/) (2022)
- [Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics](https://mlsanity.com/paper/2310.03652/) (2023)
- [Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)](https://mlsanity.com/paper/2503.05617/) (2025)
- [Calibrating constitutive models with full-field data via physics informed neural networks](https://mlsanity.com/paper/2203.16577/) (2022)
- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions](https://mlsanity.com/paper/2307.13149/) (2023)
- [Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen](https://mlsanity.com/paper/2308.11080/) (2023)
- [Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity](https://mlsanity.com/paper/2303.13634/) (2023)
- [Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2407.19326/) (2024)
- [Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling](https://mlsanity.com/paper/2410.13645/) (2024)
- [A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains](https://mlsanity.com/paper/2510.04187/) (2025)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteria](https://mlsanity.com/paper/2509.16040/) (2025)
- [COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates](https://mlsanity.com/paper/2510.00884/) (2025)
- [Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materials](https://mlsanity.com/paper/2512.01735/) (2025)
- [Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks](https://mlsanity.com/paper/2603.26517/) (2026)
- [Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables](https://mlsanity.com/paper/2308.03915/) (2023)
- [Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data](https://mlsanity.com/paper/2506.14036/) (2025)
- [Learning Physics-Consistent Material Behavior from Dynamic Displacements](https://mlsanity.com/paper/2407.20273/) (2024)
- [Bayesian sparse modeling for interpretable prediction of hydroxide ion conductivity in anion-conductive polymer membranes](https://mlsanity.com/paper/2505.19044/) (2025)
- [Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables](https://mlsanity.com/paper/2508.00959/) (2025)
- [LLM-driven design of physics-constrained constitutive models: two agents are better than one](https://mlsanity.com/paper/2605.23754/) (2026)
- [Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data](https://mlsanity.com/paper/2606.05199/) (2026)
- [CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data](https://mlsanity.com/paper/2606.14565/) (2026)
- [Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations](https://mlsanity.com/paper/2606.19375/) (2026)

## Abstract (arXiv)

We propose a new approach for data-driven automated discovery of material laws, which we call EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery), and we apply it here to the discovery of plasticity models, including arbitrarily shaped yield surfaces and isotropic and/or kinematic hardening laws. The approach is unsupervised, i.e., it requires no stress data but only full-field displacement and global force data; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a potentially large catalogue of candidate functions; it is one-shot, i.e., discovery only needs one experiment. The material model library is constructed by expanding the yield function with a Fourier series, whereas isotropic and kinematic hardening are introduced by assuming a yield function dependency on internal history variables that evolve with the plastic deformation. For selecting the most relevant Fourier modes and identifying the hardening behavior, EUCLID employs physics knowledge, i.e., the optimization problem that governs the discovery enforces the equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity promoting regularization is deployed to generate a set of solutions out of which a solution with low cost and high parsimony is automatically selected. Through virtual experiments, we demonstrate the ability of EUCLID to accurately discover several plastic yield surfaces and hardening mechanisms of different complexity.