Machine learning and data-driven methods for steel constitutive modeling: a state-of-the-art review and validation

In this work we develop and validate neural-network (NN) constitutive models for structural steels under monotonic and cyclic loading, using internal-variable inputs to encode path dependence. For monotonic tension at $$200-800^{\circ }C$$ (Kirby-Preston dataset), a feed-forward NN ( $$1-10-10-1$$ , sigmoid activation) reproduces experimental stress-strain curves to high fidelity; across temperature-specific curves extracted from the experimental data, the median normalized Chamfer distance is $$0.355\%$$ of the plot height $$(IQR: 0.026-0.361\%)$$ . For cyclic compression of stainless steel 316 (Chaboche dataset), the internal-variable NN ( $$5-30-30-1$$ ) aligns with the experimental hysteresis loops with median normalized Chamfer distance $$0.032\%$$ , indicating near-pixel-level curve overlap. We provide new quantitative validation tables and sensitivity plots; results indicate weak dependence on hidden-node count and epochs within practical ranges. The approach is computationally lightweight at inference and amenable to generalization via internal-state encoding. Limitations at very high temperatures ( $$>750^{\circ }C$$ ) and low-strain transitions are discussed, along with integration paths for physics-guided constraints.