Implementation in code_aster
============================

The number of kinematic work hardening surfaces in the model is fixed at twelve. The first eleven surfaces cover the range of shear deformations between :math:`{10}^{-5}` and :math:`\mathrm{2,0}\times {10}^{-2}`. An elastic linear behavior is considered for deformations smaller than :math:`{10}^{-5}` and a maximum shear deformation of :math:`\mathrm{2,0}\times {10}^{-2}`. The interpolation values used are as follows:


.. csv-table::

    "γ1=1.00000000e-05"
    "γ2=2.15443469e-05"
    "γ3=4.64158883e-05"
    "γ4=1.00000000e-04"
    "γ5=2.15443469e-04"
    "γ6=4.64158883e-04"
    "γ7=1.00000000e-03"
    "γ8=2.15443469e-03"
    "γ9=4.64158883e-03"
    "γ10=1.00000000e-02"
    "γ11=2.00000000e-02"


Beyond a shear deformation of :math:`\mathrm{2,0}\times {10}^{-2}`, the results of the model will be approximate because the last surface, positioned at a shear deformation of :math:`\mathrm{1,0}\times {10}^{-1}`, simply allows the model to provide a response between :math:`\mathrm{2,0}\times {10}^{-2}` and :math:`\mathrm{1,0}\times {10}^{-1}`.




.. _Ref2286161901:


Internal variables
------------------

The following internal variables (StateVariable and AuxiliaryStateVariable in language MFront) are available when calculating with Iwan's law of behavior:


.. csv-table::

    "Eel (1-6)", "Elastic deformation tensor"
    "pp (7-18)", "Vector of scalar plastic multipliers :math:`>`"
    "X (19-91)", "Kinematic work hardening tensor vector :math:`{\text{X}}_{\text{n}}`"
    "fn (92-103)", "Load surface value vector"





Model description under MFront
--------------------------------

The behavior is defined in the iwan.mfront file.


.. csv-table::

    "Parser/ DSL ", "Implicit"
    "Algorithm", "NewtonRaphson"
    "", "@Theta 1.
    @IterMax 50
    @Epsilon 1.E-12"
    "Internal variables (@StateVariable)", "real pp [1:12]"
    "Auxiliary internal variables (@AuxiliaryStateVariable)", "Stensor X [1:12]
    realfn [1:12]"
    "Command variables (@ExternalStateVariable)", "**none**"
    "Modelizations", "'3D'
    'AXIS'
    'D_ PLAN '"
    "Deformations", "'PETIT'
    'PETIT_REAC'
    'GDEF_LOG'"