<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(200-800^{\circ }C\)</EquationSource> </InlineEquation> (Kirby-Preston dataset), a feed-forward NN (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1-10-10-1\)</EquationSource> </InlineEquation>, 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(0.355\%\)</EquationSource> </InlineEquation> of the plot height <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((IQR: 0.026-0.361\%)\)</EquationSource> </InlineEquation>. For cyclic compression of stainless steel 316 (Chaboche dataset), the internal-variable NN (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(5-30-30-1\)</EquationSource> </InlineEquation>) aligns with the experimental hysteresis loops with median normalized Chamfer distance <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(0.032\%\)</EquationSource> </InlineEquation>, 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 (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(&gt;750^{\circ }C\)</EquationSource> </InlineEquation>) and low-strain transitions are discussed, along with integration paths for physics-guided constraints.</p>

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

  • Stefanos Voulgaris,
  • Spyros Chandrinos,
  • Ilias Chamatidis,
  • Giorgos Kazakis,
  • Pantelis Tsakalis,
  • Chara Ch. Mitropoulou,
  • Stelios K. Georgantzinos,
  • Denis Istrati,
  • Nikos D. Lagaros

摘要

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.