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


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


.. math::
 :label: eq-1

    \ textrm {Modeling}
    \ mathrm {2D}


.. image:: images/100007CC000069BB000067DFBB97E607D5BD7D2E.svg
    :width: 220
    :height: 216


.. _RefImage_100007CC000069BB000067DFBB97E607D5BD7D2E.svg:

Figure 4.1-1: Modeling B mesh

**Boundary conditions:**


.. math::
: label: EQ-None

    \ mathit {N1}
    \ mathit {N2}

Table 4.1-1: Boundary conditions for B modeling

**Charging:**

Traction on the face :math:`\mathrm{[}\mathrm{3,}4\mathrm{]}` (mesh SEG2)

The total number of increments is 20 (20 increments between :math:`t\mathrm{=}\mathrm{0s}` and :math:`\mathrm{2s}`)

Convergence is achieved if residue RESI_GLOB_RELA is less than or equal to 10—6.


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

Number of knots: 4

Number of meshes: 2

1 QUAD4

1 SEG2


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


+---------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+------------+-------+-------------+
|**Identification**                                                                                                                                             |**Reference**                      |**Tolerance**|
+                                                                                                                                                               +--------------+------------+-------+             +
|                                                                                                                                                               |**SIMO_MIEHE**|**GDEF_LOG**|**HPP**|             |
+---------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+------------+-------+-------------+
|:math:`t\mathrm{=}2` Displacement :math:`\mathit{DX}` (:math:`\mathit{N8}`)                                                                                    |290           |290         |290    |1.00%        |
+---------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+------------+-------+-------------+
|:math:`t\mathrm{=}2` Constraints :math:`\mathit{SIGXX}` (:math:`\mathit{PG1}`)                                                                                 |1495          |1495        |1570   |1.00%        |
+---------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+------------+-------+-------------+
|:math:`t\mathrm{=}2` Variable                                                                                                                                  |0.2475        |0.2475      |0.282  |1.50%        |
+ .. image:: images/Object_65.svg                                                                                                                               +              +            +       +             +
|    :width: 220                                                                                                                                                |              |            |       |             |
+    :height: 216                                                                                                                                               +              +            +       +             +
|                                                                                                                                                               |              |            |       |             |
+ :math:`\mathit{VARI}` (:math:`\mathit{PG1}`)                                                                                                                  +              +            +       +             +
|                                                                                                                                                               |              |            |       |             |
+---------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+------------+-------+-------------+
|:math:`t\mathrm{=}2` ENER_ELAS, TOTALE                                                                                                                         |2.82E+009     |2.81 E9     |3.08 E9|5.00%        |
+---------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------+------------+-------+-------------+

Table 4.3-1: Model B results


GDEF_LOG with ETAT_INIT
-----------------------

To impose an initial stress field in large deformations with the GDEF_LOG formalism, the user must give as input the stress tensor defined in the :math:`T` logarithmic space (and not that of Cauchy :math:`\sigma`). Since the components of the latter are stored as internal variables, it is necessary to use the operands VARI and DEPL of the keyword factor ETAT_INIT of the command STAT_NON_LINE as indicated below (these fields can for example be obtained by the command CREA_CHAMP).

We get the internal variables field (to obtain :math:`T`) and also the corresponding displacement field:

VAR_LOG1 = CREA_CHAMP (INFO =2,

TYPE_CHAM =' ELGA_VARI_R ',

OPERATION =' EXTR ',

RESULTAT = LOG1,

NOM_CHAM =' VARI_ELGA ',

INST =1.0,);

DEP_LOG1 = CREA_CHAMP (INFO =2,

TYPE_CHAM =' NOEU_DEPL_R ',

OPERATION =' EXTR ',

RESULTAT = LOG1,

NOM_CHAM =' DEPL ',

INST =1.0,);

then we enter in STAT_NON_LINE, the initial stress state:

ETAT_INIT =_F (VARI = VAR_LOG1,

DEPL = DEP_LOG1).