.. _auto_math_verify_thermodynamic_stability:

*COMPUTE MATH VALUE TO VERIFY THERMODYNAMIC STABILITY*
======================================================

Verifies thermodynamic (elastic) stability of an isotropic material by checking the consistency constraints among Young's modulus, shear modulus, and Poisson's ratio. Use this worker to validate that a material's elastic constants satisfy the necessary stability conditions before passing them to a solver or material card.

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

Classification: **process**.

Tagged: ``elastic_stability``, ``isotropic``, ``material_constants``, ``math``, ``poissons_ratio``, ``shear_modulus``, ``stability_check``, ``thermodynamic_stability``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - youngs_modulus
     - youngs_modulus
     - scalar
     - 210
     - ✓
     - Young's modulus of the material in GPa (default 210 GPa for steel); must be positive and consistent with the supplied shear modulus and Poisson's ratio for the stability check to pass.
   * - shear_modulus
     - shear_modulus
     - float
     - 80
     - ✓
     - Shear modulus of the material in GPa (default 80 GPa for steel); used together with Young's modulus and Poisson's ratio to verify the elastic stability relation G = E / (2(1+ν)).
   * - poissons_ratio
     - poissons_ratio
     - float
     - 0.3
     - ✓
     - Dimensionless Poisson's ratio of the material (default 0.3); must satisfy −1 < ν < 0.5 for a thermodynamically stable isotropic solid.

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - math_verify_thermodynamic_stability_output_1
     - math_verify_thermodynamic_stability_output_1
     - scalar
     - Scalar result of the thermodynamic stability verification — typically a numeric consistency metric or pass/fail indicator (e.g., residual of G − E/(2(1+ν))); a value near zero indicates the elastic constants are mutually consistent and thermodynamically stable.

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

- 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=math_verify_thermodynamic_stability <https://www.d3view.com/api/workflow/example?id=math_verify_thermodynamic_stability>`_

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>math_verify_thermodynamic_stability</code>. Schema hash: <code>33289d5c9cba</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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