.. _auto_curve_post_necking_fit: *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 ------ .. list-table:: :header-rows: 1 :widths: 20 20 20 20 20 20 * - 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 ------- .. list-table:: :header-rows: 1 :widths: 20 20 20 20 * - 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 ---------------- A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=curve_post_necking_fit `_ .. raw:: html

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