SURROGATE MODELING OF ELASTIC-PLASTIC SHEET METAL BENDING: A COMPARATIVE STUDY OF SURROGATE METHODS AND A DIAGNOSTIC TEST OF PHYSICS REGULARIZATION

Bohdan Petrovskyi

Abstract


Background. Sheet metal bending is a key manufacturing operation in which springback — the partial elastic recovery of the workpiece after unloading — causes deviations from the target geometry and must be predicted accurately. Repeated finite element simulations are computationally expensive for wide parametric studies, motivating fast surrogate models. This work compares surrogate modeling approaches for elastic-plastic sheet bending and evaluates the diagnostic value of a physics consistency check for detecting physically implausible neural surrogates, independently of whether physics regularization improves raw predictive accuracy.

Methods. A dataset of 39 568 finite element simulations was generated in COMSOL Multiphysics 6.2 by varying sheet thickness, punch displacement, and Young’s modulus of a 6111-T4 aluminum alloy blank. Five classical surrogate methods and three neural network models (a pure data-driven baseline, a Hollomon-regularized model with correct parameters, and a control model with intentionally incorrect parameters) were compared over 5 random data splits. A sensitivity sweep varied the control model's hardening exponent between the true and the incorrect value to test how sharply the diagnostic responds.

Results. Classical non-parametric methods slightly outperform the neural surrogates on the dense smooth parameter grid: the random forest achieves a coefficient of determination of R² > 0.9999, compared to R² ≈ 0.999 for the neural models. Differences in raw accuracy among the three neural models are statistically detectable across seeds (paired t-test) but tiny in magnitude (ΔR² < 0.1 percentage point). The physics consistency metric, in contrast, separates the models by orders of magnitude: R² = 0.999 for the correct model versus R² ≈ −2.9 for the incorrect one. The sensitivity sweep reveals a sharp threshold rather than gradual degradation: consistency remains near-perfect while the hardening exponent error stays small, then collapses once the exponent deviates substantially from its true value.

Conclusion. Standard accuracy metrics are insufficient to detect physically inconsistent neural surrogates, and the underlying diagnostic signal is thresholded rather than gradual. The physics consistency metric provides an independent diagnostic criterion that complements standard accuracy measures.

Keywords: physics-regularized neural networks; surrogate modeling; sheet metal bending; springback; Hollomon hardening law; random forest.


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DOI: http://dx.doi.org/10.30970/eli.35.8

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