Reference problem
=====================

The radius of curvature of the elbow is: :math:`{R}_{c}=\mathrm{1.25m}`

The tubular section has an average radius :math:`R=\mathrm{395.5mm}` and a thickness :math:`e=\mathrm{77mm}`.


Material properties
------------------------

The material is elastoplastic with isotropic linear work hardening.

:math:`E=2.E11\mathrm{Pa}`

:math:`\nu =0.3`

Elasticity limit :math:`\mathrm{SIGY}={200.10}^{6}\mathrm{Pa}`

Work hardening module :math:`D-\mathrm{SIGM}-\mathrm{EPSI}={2.10}^{10}\mathrm{Pa}`


Boundary conditions and loads
-------------------------------------

Embedding in :math:`A` (corresponding to the pipe section named :math:`\mathrm{CERCLE1}`).

Moment :math:`\mathrm{MZ}` imposed in :math:`D` (corresponding to :math:`\mathrm{CERCLE2}`) increasing until:


.. csv-table::

    "Increment 1"," :math:`\mathrm{Mz}=308670215.2\mathrm{Nm}`"


In the case of the calculation with large displacements, :math:`\mathrm{Mz}` is reached in 10 equal increments


Initial conditions
--------------------

Not applicable.