For an isotropic, homogeneous solid under plane stress conditions at constant temperature, as assumed in the simulation
problem description, the constitutive model for stress and strain is given by the equations :cite:`bower`

.. math::

   \sigma_{33} = \sigma_{23} = \sigma_{13} = 0

.. math::

   \sigma_{11} = \frac{E}{1 - \nu^{2}} \left ( \epsilon_{11} + \nu\epsilon_{22} \right )

   \sigma_{22} = \frac{E}{1 - \nu^{2}} \left ( \epsilon_{22} + \nu\epsilon_{11} \right )

In the case of unconstrained transverse expansion, the transverse stress :math:`\sigma_{11}` is zero and the theoretical
expected stress in the direction of the applied displacement, :math:`\sigma_{22}` is given by

.. math::

   \sigma_{22} = E \epsilon_{22}

With the material parameters from the Material Parameters Table and an applied strain of

.. math::

   \epsilon_{22} = \delta / L = -0.01 mm / 1.0 mm = -0.01 mm/mm

where :math:`L` is the nominal starting height and :math:`\delta` is the change in height, the expected stress for this
simulation is

.. math::

   \sigma_{22} = E \epsilon_{22} = \left ( 100 MPa \right ) \left ( -0.01 mm/mm \right ) = -1 MPa
