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


Calculation method
-----------------

The approach consists in combining the following calculations:


* the mechanical calculation parameters being dependent on the temperature, a thermal calculation makes it possible to determine the control variable :math:`\mathit{TEMP}`


* a mechanical calculation in linear elasticity


* an incremental elasto-plastic mechanical calculation


* calculation of the energy return rate :math:`{G}_{\mathit{ELAS}}` from the linear mechanical result, at the bottom of the crack :math:`B`


* calculation of the energy return rate :math:`{G}_{\mathit{PLAS}}` from the non-linear mechanical result, at the bottom of a crack :math:`B`

Then the margin factors are obtained by post-processing via Python using the user Python of the results of calculating the energy recovery rates :math:`{G}_{\mathit{ELAS}}` and :math:`{G}_{\mathit{PLAS}}`, and of the temperature :math:`\mathit{TEMP}` at point :math:`B`.

The following quantities are retained:


1. :math:`\mathit{KELAS}`: elastic stress intensity factor


2. :math:`\mathit{KPLAS}`: plastic stress intensity factor


3. :math:`\mathit{FM}\text{\_}\mathit{ASN}`: regulatory margin factor

These results are provided and the validation is of the "AUTRE_ASTER" type.


Reference quantities and results
-----------------------------------

The outputs of operator POST_FM are tested, namely the following quantities at the bottom of the crack:


1. :math:`\mathit{TEMP}`: temperature at the bottom of the crack


2. :math:`\mathit{KIC}`: tenacity at the bottom of a crack


3. :math:`\mathit{KELAS}`: elastic stress intensity factor


4. :math:`\mathit{KPLAS}`: plastic stress intensity factor


5. :math:`\mathit{KCP}`: corrected stress intensity factor


6. :math:`\mathit{FM}\text{\_}\mathit{ASN}`: margin factor (case DSR)


7. :math:`\mathit{FM}\text{\_}\mathit{PLAS}`: regulatory margin factor (case DDR)