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


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

The reference results are obtained by another Aster calculation.


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

The displacements, the reaction forces at different nodes of the mesh are evaluated, as well as the local stress values for different cells.

These values are obtained for three moments :math:`t`: formula formula :math:`t=1`, formula formula, formula :math:`t=2`, formula :math:`t=10`.


+---------------------------------------------------------------------------+------------------+-------------------+---------+
|**Identification**                                                         |**Reference type**|**Reference value**          |
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |Instant            |Value    |
+---------------------------------------------------------------------------+------------------+-------------------+---------+
|Formula point :math:`\mathrm{N05}` Formula travel :math:`\mathrm{DZ}`      |'AUTRE_ASTER'     |1                  |-7.06E-01|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |2                  |-1.41E+00|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |10                 |-6.50E+00|
+---------------------------------------------------------------------------+------------------+-------------------+---------+
|Formula point :math:`\mathrm{N06}` Formula travel :math:`\mathrm{DZ}`      |'AUTRE_ASTER'     |1                  |-4.81E-01|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |2                  |-9.63E-01|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |10                 |-4.86E+00|
+---------------------------------------------------------------------------+------------------+-------------------+---------+
|Formula point :math:`\mathrm{N01}` Force Nodale formula :math:`\mathrm{DX}`|'AUTRE_ASTER'     |1                  |-6.35E+09|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |2                  |-1.27E+10|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |10                 |-6.33E+10|
+---------------------------------------------------------------------------+------------------+-------------------+---------+
|Formula point :math:`\mathrm{N01}` Force Nodale formula :math:`\mathrm{DY}`|'AUTRE_ASTER'     |1                  |-6.07E+09|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |2                  |-1.21E+10|
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |10                 |-6.12E+10|
+---------------------------------------------------------------------------+------------------+-------------------+---------+
|Formula point :math:`\mathrm{N01}` Force Nodale formula :math:`\mathrm{DZ}`|'AUTRE_ASTER'     |1                  |5.72E+08 |
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |2                  |1.14E+09 |
+                                                                           +                  +-------------------+---------+
|                                                                           |                  |10                 |4.18E+09 |
+---------------------------------------------------------------------------+------------------+-------------------+---------+

Constraints in the mesh that models the membrane_grid at Gauss point number 1.

.. csv-table::

    "", "Sigxx for rebar meshes oriented according to :math:`\mathrm{OX}` ", "Sigxx for rebar meshes oriented according to :math:`\mathrm{OY}`"
    "Instant", "Reference Value", "Reference Value"
    "1", "2.94E+10", "2.00E+11"
    "2", "5.88E+10", "2.20E+11"
    "10", "2.15E+11", "3.80E+11"


Cumulative plasticity in the mesh that models the membrane_grid at the Gauss point number 1.

.. csv-table::

    "", "Internal variables V1 for rebar meshes oriented according to :math:`\mathrm{ox}` ", "Internal variables v1 for rebar meshes oriented according to :math:`\mathrm{oY}`"
    "Instant", "Reference Value", "Reference Value"
    "2", "", "9.00E-01"
    "10", "6.73E-01", "4.06E+04"


Stresses in the hexa8 concrete mesh at the Gauss point number 1: mesh :math:`\mathit{BMA1}`

+-------+---------------------------------+--------+---------+--------+
|       |Constraints: Hexa8-point mesh (1)                            |
+-------+---------------------------------+--------+---------+--------+
|Instant|Reference value                                              |
+       +---------------------------------+--------+---------+--------+
|       |SIXX                             |SIYY    |SIZZ     |SIXZ    |
+-------+---------------------------------+--------+---------+--------+
|1      |2.41E+10                         |2.41E+10|-3.52E+09|3.96E+08|
+-------+---------------------------------+--------+---------+--------+
|2      |4.82E+10                         |4.82E+10|-7.04E+09|7.91E+08|
+-------+---------------------------------+--------+---------+--------+
|10     |2.44E+11                         |2.44E+11|-2.57E+10|2.89E+09|
+-------+---------------------------------+--------+---------+--------+