Reference solution
=====================


Modeling A
---------------


Calculation method used for the reference solution
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The reference results come from the thesis of I. PAPADOPOULOS [:ref:`bib1 <bib1>`]. For the criterion of CROSSLAND, they can also be obtained manually.

Since the loading is radial, the two criteria must provide the same results.


Benchmark results
~~~~~~~~~~~~~~~~~~~~~~~~

For the **criterion of CROSSLAND**, we test the value of the splitting amplitude, the value of the maximum hydrostatic pressure and the value of the criterion:

:math:`{\tau }_{a}\mathrm{=}313.579\mathit{Mpa}` :math:`{P}_{\mathit{max}}\mathrm{=}137.\mathit{Mpa}` :math:`\mathit{Rcrit}\mathrm{=}\mathrm{-}8.281`

For the **criterion of DANG VAN - PAPADOPOULOS**, we test the value of the radius of the smallest sphere circumscribed to the load, the value of the maximum hydrostatic pressure and the value of the criterion:

:math:`{K}^{\text{*}}\mathrm{=}313.579\mathit{Mpa}` :math:`{P}_{\mathit{max}}\mathrm{=}137.\mathit{Mpa}` :math:`\mathit{Rcrit}\mathrm{=}\mathrm{-}8.281`


B, C, D, E, E, F, and G models
--------------------------------

We are based on the models calculated by CALC_FATIGUE in the SSLV135 test case. See [:ref:`V3.04.135 <V3.04.135>`] for reference solutions.


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

Analytical solutions or solutions obtained from CALC_FATIGUE.


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


1. Thesis by I. PAPADOPOULOS "Polycyclic metal fatigue: a new approach" (1987) ENPC.