.. _auto_curve_effective_variance_scales:

*COMPUTE SCALES USING THE STANDARD VARIANCE OF YIELD, ULTIMATE AND FAILURE STRESS*
==================================================================================

Computes effective variance-based scale factors for a quasi-static stress–strain curve by deriving min/max deviation scales at the yield, ultimate, and failure stress points. Given user-supplied fractional tolerances for each stress/strain landmark and the elastic modulus slope, it returns a key-value set of scale parameters suitable for downstream material scatter or stochastic analysis.

When to use
-----------

Classification: **process**.

Tagged: ``effective_stress_strain``, ``failure_stress``, ``material_calibration``, ``quasi_static``, ``scatter``, ``stochastic``, ``ultimate_stress``, ``variance_scales``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Quasi-Static Effective Stress Strain Curve
     - quasi-static_effective_stress_strain_curve
     - vector
     - —
     - 
     - The reference quasi-static effective (true) stress–strain curve (vector of [strain, stress] pairs) from which yield, ultimate, and failure landmarks are extracted; leave unconnected only if landmark stresses are fully overridden externally.
   * - QS Yield Stress Min
     - qs_yield_stress_min
     - scalar
     - -0.05
     - 
     - Lower fractional tolerance on quasi-static yield stress (e.g., -0.05 = −5 %); used to define the minimum yield-stress scale factor; default −0.05.
   * - QS Yield Stress Max
     - qs_yield_stress_max
     - scalar
     - -0.05
     - 
     - Upper fractional tolerance on quasi-static yield stress (e.g., +0.05 = +5 %); used to define the maximum yield-stress scale factor; default −0.05 (override to a positive value in practice).
   * - QS Ultimate Stress Min
     - qs_ultimate_stress_min
     - scalar
     - -0.05
     - 
     - Lower fractional tolerance on quasi-static ultimate (UTS) stress; sets the minimum UTS scale factor; default −0.05.
   * - QS Ultimate Stress Max
     - qs_ultimate_stress_max
     - scalar
     - -0.05
     - 
     - Upper fractional tolerance on quasi-static ultimate (UTS) stress; sets the maximum UTS scale factor; default −0.05 (override to a positive value in practice).
   * - QS Elongation Strain Min
     - qs_elongation_strain_min
     - scalar
     - -0.05
     - 
     - Lower fractional tolerance on quasi-static elongation (failure) strain; sets the minimum failure-strain scale factor; default −0.05.
   * - QS Elongation Strain Max
     - qs_elongation_strain_max
     - scalar
     - -0.05
     - 
     - Upper fractional tolerance on quasi-static elongation (failure) strain; sets the maximum failure-strain scale factor; default −0.05 (override to a positive value in practice).
   * - Elastic Modulus
     - elastic_modulus
     - scalar
     - 210
     - 
     - Young's modulus (GPa) of the material, used to compute the elastic slope when projecting scale deviations back onto the curve; default 210 GPa (steel).
   * - Yield Offset
     - yield_offset
     - scalar
     - 0.002
     - 
     - 

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - curve_eff_variance_scales_output_1
     - curve_eff_variance_scales_output_1
     - keyvalue
     - Key-value list of computed variance scale factors (one entry per landmark × bound combination, e.g., 'yield_min', 'yield_max', 'ultimate_min', 'ultimate_max', 'failure_min', 'failure_max'), expressed as dimensionless multipliers ready for use in stochastic or scatter-band workflows.

Disciplines
-----------

- data.curve.transform
- design_exploration.reliability
- engineering.material.calibration
- engineering.material.characterization

Runnable example
----------------

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=curve_effective_variance_scales <https://www.d3view.com/api/workflow/example?id=curve_effective_variance_scales>`_

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