Voce isotropic hardening
========================

Overview
--------

This object provides the Voce isotropic hardening.
The isotropic hardening variable is defined as

.. math::
   Q = -\sigma_0 -R \left( 1 - e^{-\delta \alpha} \right).

The model requires a single history variable (:math:`\alpha`)
and maps to a single hardening variable (:math:`Q`).

.. WARNING::
   All of the NEML yield surfaces assume the opposite of the standard
   sign convention for isotropic and kinematic hardening.
   The hardening model is expected to return a negative value of the
   isotropic hardening stress and a negative value of the backstress.

Parameters
----------

.. csv-table::
   :header: "Parameter", "Object type", "Description", "Default"
   :widths: 12, 30, 50, 8

   ``s0``, :cpp:class:`neml::Interpolate`, Initial yield stress, No
   ``R``, :cpp:class:`neml::Interpolate`, Saturated hardening increase, No
   ``d``, :cpp:class:`neml::Interpolate`, Saturation rate constant, No

Class description
-----------------

.. doxygenclass:: neml::VoceIsotropicHardeningRule
   :members:
   :undoc-members: