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


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


Geometry
---------

Straight beam, length :math:`L=\mathrm{1m}`

Circular section with radius :math:`R=\mathrm{0.01m}`.


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

Isotropic linear work hardening elastoplastic material:

Young's module: :math:`E=210000\mathrm{MPa}`

Poisson's ratio: :math:`\nu =0`. (Euler-Bernoulli beam hypothesis)

Elastic limit: :math:`{\sigma }_{Y}=4\mathrm{MPa}`

Tangent module: :math:`{E}_{T}=70000\mathrm{MPa}`


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


* Boundary conditions: embeddedness over the entire base surface


* Surface force on the upper side: at :math:`t=\mathrm{1s}`, :math:`F=6.5\mathrm{MPa}`

This load is applied in 10 equally divided time steps.