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


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

Behavior :math:`\mathrm{C2}`: linear kinematic work hardening, in :math:`\mathrm{3D}`. It is modelled in three ways:


* or using behavior VMIS_CINE_LINE, by taking:

:math:`\text{D\_SIGM\_EPSI}=\mathrm{E.C}(T)/(E+C(T))` with :math:`C(T)=(1000+\mathrm{2990.T})`


* or using behavior VMIS_ECMI_LINE, by taking:

:math:`\text{D\_SIGM\_EPSI}=\mathrm{E.C}(T)/(E+C(T))` and the Prager constant :math:`\mathrm{PRAG}=2/3C(T)`


* or using behavior VMIS_CIN1_CHAB, keeping only linear kinematic work hardening: All you have to do is then take: :math:`{R}_{0}={R}_{I}=\mathrm{SIGY}`, :math:`b=0`, :math:`{C}_{I}=C(T)`, :math:`{G}_{0}=0`

Time discretization: 1 time step between :math:`t=\mathrm{0s}` and :math:`t=\mathrm{1s}` and 20 time steps between :math:`t=\mathrm{1s}` and :math:`t=\mathrm{2s}`.


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

The mesh includes a HEXA8 mesh.


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

Behavior VMIS_CINE_LINE:


.. csv-table::

    "**Instant (** :math:`s` **)**", "**Plastic deformation by** :math:`Y` ", "**Reference**", "**Aster**", "**% difference**", "**% difference**"
    ":math:`\mathrm{t1}=1.1` "," :math:`\mathrm{EPYY}` ", "0.01", "0.01", "0."
    "2"," :math:`\mathrm{EPYY}` ", "8.E—4", "8.E—4", "0"


Behavior VMIS_ECMI_LINE:


.. csv-table::

    "**Instant (** :math:`s` **)**", "**Plastic deformation by** :math:`Y` ", "**Reference**", "**Aster**", "**% difference**", "**% difference**"
    ":math:`\mathrm{t1}=1.1` "," :math:`\mathrm{EPYY}` ", "0.01", "0.01", "0."
    "2"," :math:`\mathrm{EPYY}` ", "8.E—4", "8.E—4", "0"


Behavior VMIS_CIN1_CHAB:


.. csv-table::

    "**Instant (** :math:`s` **)**", "**Plastic deformation by** :math:`Y` ", "**Reference**", "**Aster**", "**% difference**", "**% difference**"
    ":math:`\mathrm{t1}=1.1` "," :math:`\mathrm{EPYY}` ", "0.01", "0.01", "0."
    "2"," :math:`\mathrm{EPYY}` ", "8.E—4", "8.E—4", "0"