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


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

This test is taken from the software validation manual POSTDAM version 1.0. The reference solutions are given in this document.


Benchmark results
----------------------


* **First call** to POST_FATIGUE: method RAINFLOW from :math:`{\sigma }_{1}(t)`


.. csv-table::

    "Nb_Cycl = 4", "Cycle 1", "Vale_Min:", "300. ", "Vale_Max:", "400."
    "", "Cycle 2", "Vale_Min:", "200. ", "Vale_Max:", "500."
    "", "Cycle 3", "Vale_Min:", "—300. ", "Vale_Max:", "200."
    "", "Cycle 4", "Vale_Min:", "—500. ", "Vale_Max:", "500."



* **Second call** to POST_FATIGUE: method RCCM from :math:`{\sigma }_{1}(t)`


.. csv-table::

    "Nb_Cycl = 5", "Cycle 1", "Vale_Min:", "—500. ", "Vale_Max:", "500."
    "", "Cycle 2", "Vale_Min:", "—300. ", "Vale_Max:", "500."
    "", "Cycle 3", "Vale_Min:", "0. ", "Vale_Max:", "400."
    "", "Cycle 4", "Vale_Min:", "200. ", "Vale_Max:", "300."
    "", "Cycle 5", "Vale_Min:", "88.8889", "Vale_Max:", "200."



* **Third call** to POST_FATIGUE: method RAINFLOW from :math:`{\sigma }_{2}(t)` with :math:`{K}_{T}=2`.

(Results identical to the first call to POST_FATIGUE since we take a loading :math:`{\sigma }_{2}(t)=1/2{\sigma }_{1}(t)`, then we multiply the loading history by a stress concentration coefficient :math:`{K}_{T}=2.`).


.. csv-table::

    "Nb_Cycl = 4", "Cycle 1", "Vale_Min:", "300. ", "Vale_Max:", "400."
    "", "Cycle 2", "Vale_Min:", "200. ", "Vale_Max:", "500."
    "", "Cycle 3", "Vale_Min:", "—300. ", "Vale_Max:", "200."
    "", "Cycle 4", "Vale_Min:", "—500. ", "Vale_Max:", "500."



* **Fourth call** to POST_FATIGUE: method RCCM from :math:`{\sigma }_{2}(t)` with :math:`{K}_{T}=2`.

(Results identical to the second call to POST_FATIGUE since we take a loading :math:`{\sigma }_{2}(t)=1/2{\sigma }_{1}(t)`, then we multiply the loading history by a stress concentration coefficient :math:`{K}_{T}=2.`).


.. csv-table::

    "Nb_Cycl = 5", "Cycle 1", "Vale_Min:", "—500. ", "Vale_Max:", "500."
    "", "Cycle 2", "Vale_Min:", "—300. ", "Vale_Max:", "500."
    "", "Cycle 3", "Vale_Min:", "0. ", "Vale_Max:", "400."
    "", "Cycle 4", "Vale_Min:", "200. ", "Vale_Max:", "300."
    "", "Cycle 5", "Vale_Min:", "88.8889", "Vale_Max:", "200."



Uncertainty about the solution
---------------------------

Analytical solution.


Bibliographical references
---------------------------


1. POSTDAM version 1.0 validation manual. Fournier I., Vatin E. HP‑14/93/016B