D modeling
==============


Characteristics of modeling
-----------------------------------

We test the criteria in formulas (find the results of the SSLv135f test case)


Characteristics of the mesh
----------------------------

Meshing is not required.


Tested sizes and results
------------------------------



Result obtained with the first load (**SOL_NL** of SSLV135F):

The reference value corresponds to*damage* (ENDO1) and the results were obtained using the **Basquin formula**:


+----------------------------------------------------------------------------------+------------------+-------------------+
|**Identification**                                                                |**Reference type**|**Reference value**|
+----------------------------------------------------------------------------------+------------------+-------------------+
|**Criteria**                                                                      |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |1.08363973E-05     |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{EPSN1}\mathrm{-}\mathit{EPSN2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |1.0 8363973 E-0 5  |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{ETPR1}\mathrm{-}\mathit{ETPR2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |1.06338423E-05     |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{ETEQ1}\mathrm{-}\mathit{ETEQ2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+


The reference value still corresponds to*damage* (ENDO1) and the results were obtained with **interpolation** of the Wöhler curve:


+----------------------------------------------------------------------------------+------------------+-------------------+
|**Identification**                                                                |**Reference type**|**Reference value**|
+----------------------------------------------------------------------------------+------------------+-------------------+
|**Criteria**                                                                      |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |3.26558686E-05     |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{EPSN1}\mathrm{-}\mathit{EPSN2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |3.26558686E-05     |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{ETPR1}\mathrm{-}\mathit{ETPR2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |3.21404432E-05     |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{ETEQ1}\mathrm{-}\mathit{ETEQ2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+




Result obtained with the second load (**SOL_NL2** of SSLV135F):

The reference value corresponds to*damage* (ENDO1) and the results were obtained using the **Basquin formula**:


+----------------------------------------------------------------------------------+------------------+---------------------+
|**Identification**                                                                |**Reference type**|**Reference value**  |
+----------------------------------------------------------------------------------+------------------+---------------------+
|**Criteria**                                                                      |                  |                     |
+----------------------------------------------------------------------------------+------------------+---------------------+
| .. code::                                                                        |'ANALYTIQUE'      |1.449229E-04         |
+                                                                                  +                  +                     +
|    :math:`\frac{∣\mathit{EPSN1}\mathrm{-}\mathit{EPSN2}∣}{2}`                    |                  |                     |
+----------------------------------------------------------------------------------+------------------+---------------------+
| .. code::                                                                        |'ANALYTIQUE'      | #. 449229 E-0 4     |
+                                                                                  +                  +                     +
|    :math:`\frac{∣\mathit{ETPR1}\mathrm{-}\mathit{ETPR2}∣}{2}`                    |                  |                     |
+----------------------------------------------------------------------------------+------------------+---------------------+
| .. code::                                                                        |'ANALYTIQUE'      |6.5320499E-05        |
+                                                                                  +                  +                     +
|    :math:`\frac{∣\mathit{ETEQ1}\mathrm{-}\mathit{ETEQ2}∣}{2}`                    |                  |                     |
+----------------------------------------------------------------------------------+------------------+---------------------+


The reference value still corresponds to*damage* (ENDO1) and the results were obtained with **interpolation** of the Wöhler curve:


+----------------------------------------------------------------------------------+------------------+-------------------+
|**Identification**                                                                |**Reference type**|**Reference value**|
+----------------------------------------------------------------------------------+------------------+-------------------+
|**Criteria**                                                                      |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |2.408735E-04       |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{EPSN1}\mathrm{-}\mathit{EPSN2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |2.408735 E-0 4     |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{ETPR1}\mathrm{-}\mathit{ETPR2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+


Result obtained with the third load (**SOL_NL3** of SSLV135F):

The reference value corresponds to*damage* (ENDO1) and the results were obtained using the **Basquin formula**:


+----------------------------------------------------------------------------------+------------------+-------------------+
|**Identification**                                                                |**Reference type**|**Reference value**|
+----------------------------------------------------------------------------------+------------------+-------------------+
|**Criteria**                                                                      |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |1.377855E-02       |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{EPPR1}\mathrm{-}\mathit{EPPR2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+


The reference value still corresponds to*damage* (ENDO1) and the results were obtained with **interpolation** of the Wöhler curve:


+----------------------------------------------------------------------------------+------------------+-------------------+
|**Identification**                                                                |**Reference type**|**Reference value**|
+----------------------------------------------------------------------------------+------------------+-------------------+
|**Criteria**                                                                      |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+
| .. code::                                                                        |'ANALYTIQUE'      |2.1858445E-03      |
+                                                                                  +                  +                   +
|    :math:`\frac{∣\mathit{EPPR1}\mathrm{-}\mathit{EPPR2}∣}{2}`                    |                  |                   |
+----------------------------------------------------------------------------------+------------------+-------------------+