B modeling
====


Characteristics of modeling
----

It is a hardware test. To do this, we use the SIMU_POINT_MAT command, which allows calculation on a single element, with a single integration point.

The loading path between point :math:`A` and point :math:`B` is discretized in 1 step of time. But we use a fairly recent feature that allows the time step to be re-divided if an additional criterion is not verified at convergence. Here, it is proposed to verify that at each convergence, the cumulative plastic deformation increment does not exceed 0.2 10-2. As soon as this criterion is not met, then the code automatically re-cuts the time step and starts again until this criterion is met.

As an indication, 25 calculations are thus carried out between point :math:`A` and point :math:`B`, this time discretization is therefore qualified as fine, compared to that used in modeling A.

We recall that the point :math:`A` corresponds to the instant :math:`t=\mathrm{1s}` and the point :math:`B` corresponds to the instant :math:`t=\mathrm{2s}`.


Tested sizes and results
----


.. csv-table::

    "**Identification**", "**Instants**", "**Reference**", ":math:`\text{\%}` **difference**"
    ":math:`{\varepsilon }_{\mathrm{xx}}` "," :math:`A` ", "1.4830 10—2", "—0.002"
    ":math:`{\varepsilon }_{\mathrm{xy}}` "," :math:`A` ", "1.3601 10—2", "0.003"
    ":math:`{\varepsilon }_{\mathrm{xx}}` "," :math:`B` ", "3.5265 10—2", "0.39"
    ":math:`{\varepsilon }_{\mathrm{xy}}` "," :math:`B` ", "2.0471 10—2", "1.1"


We can see graphically on the the difference in deformation :math:`{\varepsilon }_{\mathrm{xy}}` between a fine temporal discretization (modeling B) and a coarse temporal discretization (5 time steps, modeling A). This difference only exists for the non-radial part of the load (beyond point :math:`A`). We can clearly see that for modeling B, the time step becomes quite small when approaching point :math:`B`, just before the moment :math:`t=\mathrm{2s}`.


.. image:: images/1000000000000CE4000009F61AE5301230D96492.png
    :width: 5.2201in
    :height: 4.839in


.. _RefImage_1000000000000CE4000009F61AE5301230D96492.png:

Figure 4.2-1: comparison between different time discretizations