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arxiv: 2606.19375 · v1 · pith:PSJHRW24new · submitted 2026-06-12 · 💻 cs.LG · cond-mat.mtrl-sci

Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations

Hyeonbin Moon , Donghyuk Cho , Jecheon Yu , Jeong Whan Yoon , Seunghwa Ryu This is my paper

Pith reviewed 2026-06-27 04:55 UTC · model grok-4.3

classification 💻 cs.LG cond-mat.mtrl-sci
keywords yield functionconvex neural networkelastoplasticityphysics-informed learninganisotropic plasticitydata-driven discoverystress integrationdisplacement data
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The pith

A convex neural network identifies anisotropic yield functions from displacement and reaction force data alone by embedding it in elastoplastic stress integration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes a framework that discovers the yield function without stress observations, plastic strain data, or a pre-chosen parametric form. It represents the yield function as a convex neural network that enforces convexity, positive homogeneity of degree one, and tension-compression symmetry. The network is trained by placing it inside a differentiable elastoplastic stress update and minimizing a physics-informed loss on force equilibrium computed from full-field displacement measurements across several loading cases. If the approach holds, it recovers the true yield surface for standard anisotropic models such as Hill 1948 and Yld2000-2d directly from ordinary mechanical test data. Sympathetic readers would value the removal of the usual requirements for direct yield-surface measurements or many directional calibrations.

Core claim

The framework identifies the yield function as a mechanically constrained constitutive component inside elastoplastic stress integration from full-field displacement and reaction force data without requiring stress observations, plastic strain measurements, direct yield surface data, or a prescribed parametric yield function. The yield function is represented by a convex neural network enforcing convexity and positive homogeneity of degree one while imposing the assumed tension-compression symmetry, and this neural yield function is trained with a differentiable stress update and a physics-informed force equilibrium loss across multiple loading cases.

What carries the argument

Convex neural network as the yield function inside a differentiable elastoplastic stress integration trained by force equilibrium loss

If this is right

  • The recovered yield function produces accurate displacement predictions in elastoplastic finite-element simulations for the benchmark cases.
  • The method recovers yield contours for von Mises, Hill 1948, and Yld2000-2d from noisy displacement data.
  • Identification succeeds when the data provide access to plastically active stress states across multiple load cases.
  • The trained neural yield function can be replaced by a polynomial surrogate for deployment in standard simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same embedding strategy could be used to discover other rate-independent constitutive functions by replacing the yield network with a different mechanically constrained representation.
  • Extension to three-dimensional stress states would require only additional load cases that activate out-of-plane plasticity.
  • The approach supplies a route to update yield models in situ from imaging-based displacement fields during ongoing experiments.
  • If the tension-compression symmetry assumption is relaxed, the framework could address materials with asymmetric yielding.

Load-bearing premise

Training the convex neural yield function with a differentiable stress update and physics-informed force equilibrium loss across multiple loading cases is sufficient to identify the true yield function from displacement data, assuming tension-compression symmetry and access to plastically active stress states.

What would settle it

Generate synthetic displacement and force data from a known analytic yield function such as von Mises or Hill 1948 in finite-element simulations, then check whether the trained neural yield contour matches the original surface within the plastically active stress states visited by the loads; mismatch falsifies the claim.

Figures

Figures reproduced from arXiv: 2606.19375 by Donghyuk Cho, Hyeonbin Moon, Jecheon Yu, Jeong Whan Yoon, Seunghwa Ryu.

Figure 1
Figure 1. Figure 1: Schematic overview of the proposed physics-informed yield function discovery framework. Full-field dis [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Specimen geometry and loading cases used for yield function discovery. A rectangular specimen with [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Convex neural network architecture and smoothed plasticity indicator. (a) Input convex neural network [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Three benchmark yield functions. (a) Two-dimensional yield contours of the von Mises, Hill 1948, and [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Yield function discovery results under noise-free conditions. (a) Loss history for the von Mises benchmark, [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Directional anisotropy of the discovered yield functions under noise-free conditions. (a) [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Sensitivity of yield function discovery to measurement noise. Ground truth yield contours and contours [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Plastically active stress states obtained from ground truth FE simulations. For each benchmark yield [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Deep-ensemble epistemic uncertainty for the discovered yield functions. For each benchmark yield function, [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Representative polynomial surrogate modeling for finite element deployment. (a) Fitting loss history for [PITH_FULL_IMAGE:figures/full_fig_p028_10.png] view at source ↗
read the original abstract

Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial. This study proposes a physics-informed framework for discovering yield functions from full-field displacement data and reaction force data, without stress observations, plastic strain measurements, direct yield surface data, or a prescribed parametric yield function. The framework identifies the yield function as a mechanically constrained constitutive component inside elastoplastic stress integration, rather than through direct stress-space supervision. The yield function is represented by a convex neural network that enforces convexity and positive homogeneity of degree one while imposing the assumed tension-compression symmetry, and this neural yield function is trained with a differentiable stress update and a physics-informed force equilibrium loss across multiple loading cases. The proposed framework is validated using finite element (FE) benchmark studies with von Mises, Hill 1948, and Yld2000-2d yield functions, assessing yield contour agreement, displacement-noise sensitivity, identifiability through plastically active stress states, epistemic uncertainty, and polynomial-surrogate deployment. This study provides a mechanics-constrained pathway for discovering anisotropic yield functions from displacement and force data while keeping the identified component within the structure of elastoplastic stress integration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims to introduce a physics-informed framework for discovering anisotropic yield functions from full-field displacement and reaction force data using convex neural networks. The yield function is embedded in a differentiable elastoplastic stress integration, trained via force equilibrium loss without needing stress observations or prescribed parametric forms. Validation is performed on finite element benchmarks with von Mises, Hill 1948, and Yld2000-2d yield functions, evaluating contour agreement, noise sensitivity, identifiability, uncertainty, and surrogate deployment.

Significance. If the central claim holds, this work offers a significant advancement in constitutive model discovery for plasticity by integrating mechanical constraints directly into the learning process. The use of convex neural representations enforcing positive homogeneity and tension-compression symmetry, combined with differentiable return mapping, allows identification from standard experimental data types. This could reduce reliance on analytical forms and direct yield surface measurements. The benchmark studies provide evidence of feasibility on synthetic data.

major comments (2)
  1. [Abstract] Abstract and identifiability assessment: the claim that the framework recovers the true yield function (rather than any convex function consistent with the data) rests on the physics-informed loss across multiple loading cases being sufficient for unique identification. The described validation via plastically active states does not include explicit tests such as recovery of a deliberately perturbed yield function or cross-validation on held-out loadings, leaving open the possibility of non-uniqueness in the loss landscape.
  2. [Validation studies] Validation studies (FE benchmarks): while yield contour agreement is reported for von Mises, Hill 1948, and Yld2000-2d cases, the manuscript does not quantify how the inferred stress states span the yield surface or demonstrate that the equilibrium residual loss is injective with respect to the neural parameters under the imposed symmetry and convexity constraints.
minor comments (1)
  1. [Abstract] The abstract refers to 'epistemic uncertainty' quantification but provides no detail on the method used (e.g., ensemble variance or Bayesian approximation) or how it is visualized in the results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and will incorporate revisions to strengthen the identifiability assessment and validation as described.

read point-by-point responses

  1. Referee: [Abstract] Abstract and identifiability assessment: the claim that the framework recovers the true yield function (rather than any convex function consistent with the data) rests on the physics-informed loss across multiple loading cases being sufficient for unique identification. The described validation via plastically active states does not include explicit tests such as recovery of a deliberately perturbed yield function or cross-validation on held-out loadings, leaving open the possibility of non-uniqueness in the loss landscape.

    Authors: We agree that the current validation relies on recovery across benchmarks with known yield functions and plastically active states but does not include the explicit uniqueness tests suggested. In the revised manuscript we will add cross-validation on held-out loading cases (withheld from training) and a perturbation test in which a deliberately modified yield function is used to generate data and recovery is attempted, to demonstrate that the physics-informed loss selects the true function under the convexity and symmetry constraints. revision: yes

  2. Referee: [Validation studies] Validation studies (FE benchmarks): while yield contour agreement is reported for von Mises, Hill 1948, and Yld2000-2d cases, the manuscript does not quantify how the inferred stress states span the yield surface or demonstrate that the equilibrium residual loss is injective with respect to the neural parameters under the imposed symmetry and convexity constraints.

    Authors: We will revise the validation section to include quantitative measures (e.g., histograms or coverage metrics) of how the inferred stress states from the training loadings populate the yield surface in principal stress space for each benchmark. We will also add a discussion of injectivity, showing that the combination of positive homogeneity, convexity, tension-compression symmetry, and the multi-case equilibrium loss constrains the neural parameters sufficiently to recover the target function in the reported benchmarks; if feasible we will include a simple numerical sensitivity check on parameter perturbations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in external force equilibrium data across independent loadings.

full rationale

The paper trains a convex neural representation of the yield function by minimizing a physics-informed loss that enforces force equilibrium on observed displacement and reaction force data from multiple loading cases, using a differentiable return-mapping procedure. This loss is computed from external benchmark FE data (von Mises, Hill 1948, Yld2000-2d) and is not equivalent to the network parameters by construction. No self-definitional steps appear (e.g., no quantity defined in terms of itself), no fitted inputs are relabeled as predictions, and no load-bearing self-citations or uniqueness theorems imported from prior author work are invoked in the provided text. The framework remains self-contained against the external data and benchmark validations, with identifiability assessed empirically via plastically active states rather than by definitional reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim depends on the neural network being able to capture the yield behavior through the constrained training process.

free parameters (1)
  • neural network parameters
    Weights and biases of the convex neural network are fitted to the data via the physics-informed loss.
axioms (2)
  • domain assumption The yield function must be convex and positively homogeneous of degree one
    Standard requirement in plasticity theory, enforced in the neural representation.
  • domain assumption Tension-compression symmetry holds for the material
    Assumed and imposed on the neural yield function as stated in the abstract.
invented entities (1)
  • Convex neural network for yield function no independent evidence
    purpose: To represent arbitrary anisotropic yield functions without a fixed parametric form while enforcing required properties
    The paper introduces this representation as part of the framework.

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discussion (0)

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