Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

The reference solution is a numerical solution resulting from a validation note for simplified methods in fracture mechanics [:ref:`bib1 <bib1>`]. The results of the reference score were obtained with code_aster version 6.06.

     [:ref:`bib1 <bib1>`] gives the value of :math:`{J}_{\text{fond}}` for different loading levels :math:`M` and :math:`P`.



The results are shown in the following table:


.. csv-table::

    ":math:`P(\mathit{MPa})` "," :math:`M(\mathit{kN}\mathrm{.}m)` "," :math:`{J}_{\text{fond}}(\mathit{kJ}/m\mathrm{²})`"
    "", "", ""
    "36.97", "-5989.46", "2.71 102"




     Where:

     :math:`{J}_{\text{fond}}(\mathit{kJ}/m\mathrm{²})` is the value of the integral J at the bottom of the crack.


Bibliography
-------------


1. P. LE DELLIOU: Code RSE -M: finite element calculations of straight pipes with longitudinal semi-elliptical defects loaded with pressure plus moment. EDF R&D. 2005. 1998.