.. _auto_curve_effective_modified_hocket_sherby:

*MODIFIED HOCKET SHERBY EXTRAPOLATION*
======================================

Extrapolates a true stress–true strain curve beyond the measured range using the Modified Hockett–Sherby hardening law: σ = A − (A − B)·exp(−C·εⁿ) + D·ε. Supply the five model parameters (A, B, C, H, D) along with the target end strain and step increment to generate a smooth extrapolated flow curve.

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

Classification: **process**.

Tagged: ``curve-fitting``, ``extrapolation``, ``flow-curve``, ``hardening-law``, ``hockett-sherby``, ``material-model``, ``modified-hockett-sherby``, ``stress-strain``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve In
     - curve_in
     - vector
     - —
     - 
     - Input true stress–true strain curve (vector of [strain, stress] pairs) whose measured range will be extended; optional if all model parameters are provided directly.
   * - A
     - a
     - scalar
     - 0.0
     - 
     - Saturation stress parameter A (MPa) — the upper asymptote of the Modified Hockett–Sherby flow stress; defaults to 0.0.
   * - B
     - b
     - scalar
     - 0.0
     - 
     - Initial yield-like stress parameter B (MPa) — sets the stress level at zero strain in the model; defaults to 0.0.
   * - C
     - c
     - scalar
     - 0.0
     - 
     - Rate parameter C (dimensionless) — controls how quickly the flow stress saturates with increasing strain; defaults to 0.0.
   * - H
     - h
     - scalar
     - 0.0
     - 
     - Exponent parameter H (dimensionless) — governs the shape (curvature) of the hardening transition in the exponential term; defaults to 0.0.
   * - D
     - d
     - scalar
     - 0.0
     - 
     - Linear hardening coefficient D (MPa) — adds a linear strain-hardening contribution on top of the saturating term; defaults to 0.0.
   * - Last Strain
     - last_strain
     - scalar
     - 1.0
     - 
     - Maximum true plastic strain to which the curve is extrapolated (dimensionless); defaults to 1.0.
   * - Increment
     - increment
     - scalar
     - 0.001
     - 
     - Strain step size used to generate discrete points along the extrapolated curve (dimensionless); defaults to 0.001 — reduce for smoother output or increase for faster computation.

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - curve_effective_modified_hocket_sherby_output_1
     - curve_effective_modified_hocket_sherby_output_1
     - vector
     - Extrapolated true stress–true strain curve (vector of [strain, stress] pairs) evaluated from the input range up to Last Strain at the specified increment using the Modified Hockett–Sherby model.

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

- data.curve.transform
- 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_modified_hocket_sherby <https://www.d3view.com/api/workflow/example?id=curve_effective_modified_hocket_sherby>`_

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