D modeling
==============


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

The calculation is repeated with the viscoplastic model (ROUSS_VISC) in modeling A, adding viscous regularization (REGU_VISC).

Two parameters must be determined for this mechanism of regulation by viscoelasticity:


* stiffness k: the apparent stiffness (k+ negative work hardening) must always be positive. If k is not big enough, we can end up in the situation where there would be no solution, even with viscosity. In this modeling, :math:`k` is chosen at the value of the Young's modulus :math:`E=2.e5\mathit{MPa}`.


* The characteristic time :math:`\mathrm{\tau }`: we first estimate the deformation rate at each point in such a nice situation. At this rate of deformation, it takes a certain amount of time to cross the elastic domain. :math:`\mathrm{\tau }` must be small (1 to 10%) compared to this time. More details will be in the internal note EDF R&D 6125-1724-2020-01606. In this modeling, the displacement of 10 mm is imposed along the length side (Y direction) by 10 mm for 10 s. This requires approximately 1.35e-4 s to reach 10% of the elastic limit (27 MPa). The value 1.0e-4 s is chosen for :math:`\mathrm{\tau }`.


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


+---------------------------+------------------------------------------------------------------------------------------------------------------------------------------+
|Model                      |*Aster_code*                                                                                                                              |
+---------------------------+------------------------------------------------------------------------------------------------------------------------------------------+
|                           |porosity                                                                                                                                  |
+                           +                                                                                                                                          +
|                           |                                                                                                                                          |
+                           + .. image:: images/Object_55.svg                                                                                                          +
|                           |    :width: 15                                                                                                                            |
+                           +    :height: 21                                                                                                                           +
|                           |                                                                                                                                          |
+                           +                                                                                                                                          +
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+                           +                                                                                                                                          +
|                           |                                                                                                                                          |
+                           + (:math:`t=10s.`)                                                                                                                         +
|                           |                                                                                                                                          |
+---------------------------+------------------------------------------------------------------------------------------------------------------------------------------+
|Viscoplastic model (= 0.57)|0.03352194                                                                                                                                |
+---------------------------+------------------------------------------------------------------------------------------------------------------------------------------+