Modeling A
==============

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

C_ PLAN modeling. 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 = :math:`\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`


* 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 QUAD4 mesh


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

.. csv-table::

    "**Behavior**", "**Instant**", "**Deformation and Stress**", "**Reference**", "**Aster**", "**% difference**"
    "VMIS_CINE_LINE ", "1.1"," EPYY ", "0.01", "0.01", "0.01", "0."
    "", "2"," EPYY ", "8.E—4", "8.E—4", "0"
    "", "1. "," SIYY ", "210", "210", "0"
    "", "1"," SIZZ ", "0. ", "5.e—7", "5.e—7"
    "VMIS_ECMI_LINE ", "t1=1.1"," EPYY "," ", "0.01", "0.01", "0."
    "", "2"," EPYY ", "8.E—4", "8.E—4", "0"
    "", "1. "," SIYY ", "210", "210", "0"
    "", "1"," SIZZ ", "0. ", "0. ", "0."
    "VMIS_CIN1_CHAB ", "t1=1.1"," EPYY "," ", "0.01", "0.01", "0."
    "", "2"," EPYY ", "8.E—4", "8.E—4", "0"
    "", "1. "," SIYY ", "210", "210", "0"
    "", "1"," SIZZ ", "0. ", "5.e—7", "5.e—7"
    "VMIS_CIN2_CHAB ", "t1=1.1"," EPYY "," ", "0.01", "0.01", "0."
    "", "2"," EPYY ", "8.E—4", "8.E—4", "0"
    "", "1. "," SIYY ", "210", "210", "0"
    "", "1"," SIZZ ", "0. ", "2.8.e—5", "2.8.e—5"