B modeling
==============

Case with linear kinematic work hardening.


Thermal loading for B modeling
--------------------------------------------

Reference temperature: 50°C

Loading history: :math:`{\mathrm{Evolution}}_{B}` (cf. [§1.4)

The temperatures came in like a knotty field.


Results
---------

The values of :math:`\mathit{SIXX}` are recorded at the node :math:`\mathrm{NO1}` (direction of the longitudinal reinforcements) and :math:`\mathit{SIXX}` at the node :math:`\mathrm{NO1}` (direction of the transverse reinforcements)


+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|       |:math:`\mathit{SIXX}` in meshes modeling fibers oriented according to :math:`\mathrm{OX}`                   |:math:`\mathit{SIXX}` in meshes modeling fibers oriented according to :math:`\mathrm{OY}`                   |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|Instant|Reference                                                                                |*Aster_code*|Ecart|Reference                                                                                |*Aster_code*|Ecart|
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|1      |2.00E+08                                                                                 |2.00E+08    |0    |2.00E+08                                                                                 |2.00E+08    |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|2      |2.40E+08                                                                                 |2.40E+08    |0    |2.40E+08                                                                                 |2.40E+08    |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|3      |4.00E+07                                                                                 |4.00E+07    |0    |4.00E+07                                                                                 |4.00E+07    |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|4      |2.40E+08                                                                                 |2.40E+08    |0    |2.40E+08                                                                                 |2.40E+08    |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|5      |—1,60E+08                                                                                |—1,60E+08   |0    |—1,60E+08                                                                                |—1,60E+08   |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|6      |—2.40E+08                                                                                |—2.40E+08   |0    |—2.40E+08                                                                                |—2.40E+08   |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|7      |1.60E+08                                                                                 |1.60E+08    |0    |1.60E+08                                                                                 |1.60E+08    |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|8      |2,80E+08                                                                                 |2,80E+08    |0    |2,80E+08                                                                                 |2,80E+08    |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|9      |—1,20E+08                                                                                |—1,20E+08   |0    |—1,20E+08                                                                                |—1,20E+08   |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|10     |—3.00E+08                                                                                |—3.00E+08   |0    |—3.00E+08                                                                                |—3.00E+08   |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+
|11     |1.00E+08                                                                                 |1.00E+08    |0    |1.00E+08                                                                                 |1.00E+08    |0    |
+-------+-----------------------------------------------------------------------------------------+------------+-----+-----------------------------------------------------------------------------------------+------------+-----+

**Notes:**

*The results shown are given in the reference frame* :math:`({X}_{\mathrm{ref}},{Y}_{\mathrm{ref}})` *making an angle of* :math:`0°` *with respect to* :math:`(X,Y)` *.*

*The test case studied corresponds to the following diagram in a stress-deformation plane:*


.. image:: images/Object_18.svg
    :width: 408
    :height: 274


.. _RefImage_Object_18.svg: