FIT POST-NECKING EXTRAPOLATION

Fits multiple analytical post-necking extrapolation laws (Swift, Voce, Hocket-Sherby, Mixed Swift+Voce, Stoughton-Yoon, Ludwik, Voce+Linear, Mixed Hardening) to a hardening curve by DOE-sampling each method’s parameter space and scoring candidates via squared-error curve matching. Optionally refines the search with a dense DOE pass or an ML surrogate. Returns the best-fitting method, its parameters, the fitted curve, and a per-method summary table.

When to use

Tagged: DEFINE_CURVE_STRESS, LS-DYNA, curve-fitting, doe, extrapolation, hardening, hocket-sherby, lhs.

Inputs

Label ID Type Default Required Description
Hardening Curve eff_curve vector Hardening curve as plastic strain (X) vs. effective stress (Y); must extend past the necking point so the post-necking region is available for fitting — this is the only required input.
Modulus modulus scalar 210000   Elastic (Young’s) modulus in the same stress units as eff_curve (default 210000 MPa); used to recover engineering stress-strain for statistics and to compute the effective necking strain.
Yield Offset yield_offset scalar 0.002   Offset strain for 0.2%-style yield detection (default 0.002); rarely needs changing unless a non-standard offset convention is required.
Necking Strain necking_strain scalar   Effective plastic strain at the onset of necking; if left blank the value is auto-detected from the engineering stress-strain statistics via eff_necking_strain.
Methods methods select swift,voce,hocket_sherby,mixed,stoughton_yoon,ludwik,voce_linear,mixed_hardening   Subset of analytical extrapolation forms to evaluate; defaults to all available methods — deselect methods to speed up the search or to constrain results to physically appropriate laws for the material.
Sampling Type sampling_type select lhs   DOE strategy used to explore each method’s parameter space (default LHS); LHS and Space-Filling give good coverage with fewer points, Full-Factorial can be expensive for high-dimensional parameter sets.
Points Per Variable num_points_per_variable scalar 5   Number of DOE levels per parameter variable (default 5); higher values increase coverage but multiply evaluation cost — used together with num_experiments to control total sample count.
Number of Experiments num_experiments scalar 25   Total number of DOE candidate samples to evaluate per method (default 25); increase for finer coverage at the cost of runtime.
Match Type match_type select squared   Error metric used to score curve candidates against the reference post-necking region (default ‘squared’); ‘squared’ corresponds to sum-of-squared-errors between fitted and reference stress values.
Digitize Points num_dig_points scalar 50   Number of discrete strain points used when reconstructing each candidate’s extrapolated curve for scoring (default 50); higher values give smoother curves at marginal extra cost.
Use ML Meta-Model use_ml select no   Refinement strategy after the initial DOE pass: ‘no’ (default) uses only DOE, ‘dense_doe’ augments with a larger LHS grid, ‘ml_surrogate’ trains a regression surrogate and iteratively refines the search.
ML Dense Samples ml_dense_samples scalar 200   Number of additional LHS samples added when use_ml=’dense_doe’ (default 200); ignored when use_ml=’no’ or ‘ml_surrogate’.
ML Regression Types ml_regression_types select gpr_regression,rfr_regression,gboostr_regression   Comma-separated list of surrogate regression algorithms to try when use_ml=’ml_surrogate’ (default: GPR, Random Forest, Gradient Boosting); ignored unless use_ml=’ml_surrogate’.
ML Refinement Iterations ml_iterations scalar 1   Number of surrogate-guided refinement iterations when use_ml=’ml_surrogate’ (default 1); more iterations can improve accuracy but increase runtime.
Last Strain last_strain scalar 1.0   Maximum effective plastic strain to which the fitted extrapolation is extended when generating the output best_curve (default 1.0); set to match the strain range required by the downstream material card.
Include Per-Sample Curves include_curves_in_output select no   Set to ‘yes’ to embed the full extrapolated hardening curve for every DOE sample in the all_samples output dataset; leave as ‘no’ (default) to keep the dataset compact.
Include Necking Treatment Output include_necking_treatment_output select no   Set to ‘yes’ to emit the necking_treatment output dataset in the array format accepted by curve_truetoeffectivestress; leave as ‘no’ (default) if that downstream worker is not used.
Variable Range Overrides variable_ranges dataset (complex)   Optional dataset with columns {name, min_sf, max_sf} that apply multiplicative scale factors to the built-in parameter bounds for each DOE variable; leave empty to use the default bounds derived from the input curve.

Outputs

Label ID Type Description
Best Method best_method text  
Best Parameters best_parameters keyvalue  
Best Error best_error scalar  
Best Fitted Curve best_curve vector  
Per-Method Best all_methods_summary dataset  
All DOE Samples all_samples dataset One row per evaluated candidate. Columns: method (extrapolation type), sample_id, error, last_y, plus each method’s parameters. When include_curves_in_output=yes also includes a hardening_curve column with the extrapolated curve.
Effective Necking Strain effective_necking_strain scalar  
Necking Treatment (for curve_truetoeffectivestress) necking_treatment dataset Only produced when include_necking_treatment_output=yes. Dataset of best-fit rows (expression + parameter columns) in the exact array format that curve_truetoeffectivestress’s necking_treatment input accepts. Wire directly into that input to re-apply the fitted analytical form.

Disciplines

  • ai_ml.surrogate
  • data.curve.pair
  • data.curve.transform
  • design_exploration.doe
  • engineering.material.calibration
  • engineering.material.characterization
  • engineering.material.failure

Runnable example

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