Modeling I
==============


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

Plane stress modeling in plasticity using MFront (linear isotropic work hardening plasticity). The DeBorst algorithm is activated.



.. image:: images/100000000000013200000111F70B98F1C49A635E.png
    :width: 1.7102in
    :height: 1.4929in


.. _RefImage_100000000000013200000111F70B98F1C49A635E.png:


* Dirichlet condition (keyword DDL_IMPO):


* Node :math:`\mathrm{N04}`, :math:`x=y=0`,


* Knots :math:`\mathrm{N02}`, :math:`\mathit{NS2}` :math:`x=0`.


* Neumann condition, surface forces (keyword FORCE_CONTOUR):


* on the faces (skin elements): (1, 2), (2, 4), (4, 3) and (3, 1).


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

Number of knots: 8

Number of meshes and types: 1 QUAD8, 4 SEG3


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

Following sheet 7461, we test in non-regression that the internal variables are not modified by the calculation of the energy.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**"
    "V7 at time :math:`A` ", "'NON_REGRESSION'", "0.020547265463595"



.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    ":math:`{\sigma }_{\mathrm{xx}}` at the moment :math:`A` ", "'ANALYTIQUE'", "1,512E+002"," 0.1%"
    ":math:`{\sigma }_{\mathrm{xy}}` at the moment :math:`A` ", "'ANALYTIQUE'", "9,310E+001"," 0.1%"
    ":math:`{\varepsilon }_{\mathrm{xx}}` at the moment :math:`A` ", "'ANALYTIQUE'", "1.48297E-002"," 0.1%"
    ":math:`{\varepsilon }_{\mathrm{xy}}` at the moment :math:`A` ", "'ANALYTIQUE'", "1.36014E-002"," 0.1%"
    ":math:`{\varepsilon }_{\mathrm{xx}}^{p}` at the moment :math:`B` ", "'ANALYTIQUE'", "1.4054E-002"," 1.0%"
    ":math:`{\varepsilon }_{\mathrm{xy}}^{p}` at the moment :math:`B` ", "'ANALYTIQUE'", "1, 2981E-002"," 1.0%"
    ":math:`{\varepsilon }_{\mathit{xx}}` at the moment :math:`B` ", "'ANALYTIQUE'", "3,5265E-002"," 1,0%"
    ":math:`{\varepsilon }_{\mathit{xy}}` at the moment :math:`B` ", "'ANALYTIQUE'", "2,0471E-002"," 1.0%"
    ":math:`{\varepsilon }_{\mathrm{xx}}^{p}` at the moment :math:`B` ", "'ANALYTIQUE'", "3,3946E-002"," 1.0%"
    ":math:`{\varepsilon }_{\mathrm{xy}}^{p}` at the moment :math:`B` ", "'ANALYTIQUE'", "2,0250E-002"," 1.0%"
    ":math:`p` at the moment :math:`B` ", "'ANALYTIQUE'", "4,23293E-002"," 1.0%"
    "Triaxiality rate :math:`\mathit{TRIAX}` at time :math:`A` ", "'ANALYTIQUE'", "2.2800E-001"," 0.1%"
    "Triaxiality rate :math:`\mathit{TRIAX}` at time :math:`B` ", "'ANALYTIQUE'", "3.25349E-001"," 0.1%"