Identification
==============

In addition to thermo-elastic parameters :math:`E,\nu ,\alpha`, the MAZARS Revisited model involves 6 material parameters: :math:`{A}_{c},{B}_{c},{A}_{t},{B}_{t},{\varepsilon }_{\mathit{d0}},k`.

• :math:`{\varepsilon }_{\mathrm{d0}}` is the damage threshold. It obviously acts on the peak stress but also on the shape of the post-peak curve. In fact, the drop in stress is all the less sudden the smaller :math:`{\varepsilon }_{\mathrm{d0}}` is. In general :math:`{\varepsilon }_{\mathrm{d0}}` is included in :math:`0.5` and :math:`1.5{10}^{\mathrm{-}4}`.

The coefficients :math:`A` and :math:`B` make it possible to modulate the shape of the post-peak curve. They are defined by the equations and depend on the parameters of the Mazars Origin Model (:math:`{A}_{t}`, :math:`{B}_{t}`, :math:`{A}_{c}` and :math:`{B}_{c}`) and on :math:`r`:

• :math:`A` introduces a horizontal asymptote which is the :math:`\varepsilon` axis for :math:`A\mathrm{=}1` and the horizontal passing through the peak for :math:`A\mathrm{=}0` (cf. []). In the field of traction, :math:`A` is equivalent to :math:`{A}_{t}` (and vice versa in the field of compressions :math:`A={A}_{c}`). In general, :math:`{A}_{c}` is between 1 and 2. and :math:`{A}_{t}` between 0.7 and 1.

• :math:`B` depending on its value can correspond to a sudden drop in stress (:math:`B>10000`) or a preliminary phase of stress increase followed, after passing through a maximum, by a more or less rapid decrease as can be seen on the []. In the field of traction, :math:`B` is equivalent to :math:`{B}_{t}` (and vice versa in the field of compressions :math:`B={B}_{c}`). In general :math:`{B}_{c}` is between :math:`1000` and :math:`2000` and :math:`{B}_{t}` between :math:`9000` and :math:`21000`.

• :math:`k` introduces a horizontal asymptote in pure shear on the stress-strain curve if its value is different from 1 for :math:`{A}_{t}=1`,. The recommended value is :math:`0.7`.


.. image:: images/100000000000065E00000426889D77B595B8458E.png
    :width: 4.8626in
    :height: 2.9209in


.. _RefImage_100000000000065E00000426889D77B595B8458E.png:

**Fig** figure 3-1: Influence of the parameter :math:`{A}_{t}`


.. image:: images/10000000000006640000066FFC2E6A67BFC0DF45.png
    :width: 4.6264in
    :height: 4.0181in


.. _RefImage_10000000000006640000066FFC2E6A67BFC0DF45.png:

**Fig** ure 3-2: Influence of the parameter :math:`{B}_{t}`

One way to obtain a set of parameters is to have the results of uniaxial compression and tension tests available (for traction, other types of tests can be used, "Brazilian" splitting tests for example).

If deformation gradient regularization is used (see § :ref:`1.2 <section1-2>`), it is recommended to set the parameters of the law at the same time as the characteristic length :math:`{L}_{c}`. Some authors (confer) also suggest calibrating :math:`{L}_{c}` by using experimental tests on several sizes of specimens; in fact, the characteristic length is linked to the size of the energy dissipation zone which could be at the origin of structural scale effects.