C modeling
==============

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

Modeling COQUE_3D. Unit thickness (to find the same reference solutions as the C_ PLAN case). The linear kinematic work hardening behavior is modelled in four ways:


* or using behavior VMIS_CINE_LINE, by taking:

D_ SIGM_EPSI = :math:`\mathrm{E.C}(T)/(E+C(T))` with :math:`C(T)=(1000+\mathrm{2990.T})`


* or using behavior VMIS_ECMI_LINE, by taking:

D_ SIGM_EPSI = 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`


* or using behavior VMIS_CIN2_CHAB, by choosing the parameters in such a way that the two kinematic variables are identical: All you have to do is then take:

:math:`{R}_{0}={R}_{I}=\mathrm{SIGY}`, :math:`b=0`, :math:`{\mathrm{C1}}_{I}={\mathrm{C2}}_{I}=C(T)/2`, :math:`{\mathrm{G1}}_{0}={\mathrm{G2}}_{0}=0`

Temporal discretization: 1 time step between :math:`t=\mathrm{0s}` and :math:`t=\mathrm{1s}` and 40 time steps between :math:`t=\mathrm{1s}` and :math:`t=\mathrm{2s}`.


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

The mesh includes a QUAD8 mesh


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

.. csv-table::

    "**Behavior**", "**Moment**", "**Movement and effort**", "**Reference**", "**Aster**", "**% difference**"
    "VMIS_CINE_LINE ", "1"," NYY ", "210", "210", "0"
    "", "1", "DY", "1.105 10—2", "1.105 10—2", "0"
    "", "1.1", "DY", "1.115 10—2", "1.115 10—2", "0"
    "", "2", "DY", "2.85 10—3", "2.85 10—3", "0"
    "VMIS_ECMI_LINE ", "1"," NYY ", "210", "210", "0"
    "", "1", "DY", "1.105 10—2", "1.105 10—2", "0"
    "", "1.1", "DY", "1.115 10—2", "1.115 10—2", "0"
    "", "2", "DY", "2.85 10—3", "2.85 10—3", "0"
    "VMIS_CIN1_CHAB ", "1"," NYY ", "210", "210", "0"
    "", "1", "DY", "1.105 10—2", "1.105 10—2", "0"
    "", "1.1", "DY", "1.115 10—2", "1.115 10—2", "0"
    "", "2", "DY", "2.85 10—3", "2.85 10—3", "0"
    "VMIS_CIN2_CHAB ", "1"," NYY ", "210", "210", "0"
    "", "1", "DY", "1.105 10—2", "1.105 10—2", "0"
    "", "1.1", "DY", "1.115 10—2", "1.115 10—2", "0"
    "", "2", "DY", "2.85 10—3", "2.85 10—3", "0"