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


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


* Displacement :math:`\mathrm{DY}`

The displacement :math:`\mathrm{DY}` referring to point :math:`C` corresponds to the imposed displacement.

 :math:`\mathrm{DY}=-0.015(t-1)`


* Constraint :math:`\mathrm{SIXX}`

Constraint :math:`\mathrm{SIXX}` corresponds to the load applied


* Stress :math:`\mathrm{SIYY}` and cumulative plastic deformation :math:`\mathrm{V1}`

The reference values for stress :math:`\mathrm{SIYY}` and cumulative plastic deformation :math:`\mathrm{V1}` are non-regression values.


Reference quantities
----------------------


* Constraint :math:`\mathrm{SIXX}` at point :math:`C`


* Constraint :math:`\mathrm{SIYY}` at point :math:`C`


* Cumulative plastic deformation :math:`\mathrm{V1}` at point :math:`C`


* Move :math:`\mathrm{DY}` to point :math:`C`


Benchmark result
----------------------


+----------------------------------+---------+---------------------+------------------------+------------------------+
|Grandeur                          |Point    |:math:`\mathrm{Inst}`|Reference*              |Reference**             |
+----------------------------------+---------+---------------------+------------------------+------------------------+
|:math:`\mathrm{SIXX}(\mathrm{Pa})`|:math:`C`|:math:`2.0`          |:math:`-2.0\mathrm{E6}` |:math:`-2.0\mathrm{E6}` |
+----------------------------------+---------+---------------------+------------------------+------------------------+
|:math:`\mathrm{SIYY}(\mathrm{Pa})`|:math:`C`|:math:`1.07`         |:math:`-8.69\mathrm{E6}`|:math:`-8.69\mathrm{E6}`|
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.16`         |:math:`-1.39\mathrm{E7}`|:math:`-1.37\mathrm{E7}`|
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.34`         |:math:`-9.90\mathrm{E6}`|:math:`-9.90\mathrm{E6}`|
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.53`         |:math:`-9.91\mathrm{E6}`|:math:`-9.90\mathrm{E6}`|
+----------------------------------+---------+---------------------+------------------------+------------------------+
|:math:`\mathrm{V1}`               |:math:`C`|:math:`1.07`         |:math:`0`               |:math:`0`               |
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.16`         |:math:`1.20E-3`         |:math:`1.26E-3`         |
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.34`         |:math:`1.12E-2`         |:math:`1.12E-2`         |
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.53`         |:math:`2.01E-2`         |:math:`2.01E-2`         |
+----------------------------------+---------+---------------------+------------------------+------------------------+
|:math:`\mathrm{DY}(m)`            |:math:`C`|:math:`1.07`         |:math:`-1.05E-3`        |:math:`-1.05E-3`        |
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.16`         |:math:`-2.40E-3`        |:math:`-2.40E-3`        |
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.34`         |:math:`-5.10E-3`        |:math:`-5.10E-3`        |
+                                  +         +---------------------+------------------------+------------------------+
|                                  |         |:math:`1.53`         |:math:`-7.95E-3`        |:math:`-7.95E-3`        |
+----------------------------------+---------+---------------------+------------------------+------------------------+

*linear work hardening** parabolic work hardening


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


* Analytical solution for quantities :math:`\mathrm{DY}` and :math:`\mathrm{SIXX}`


* Digital solution for sizes :math:`\mathrm{SIYY}` and :math:`\mathrm{V1}`