Reference problem
=====================


Geometry
---------

To validate the cohesive law CZM_EXP_MIX, which is more specific to almost fragile materials, we model a notched concrete beam subjected to 3-point bending, based on the experimental data from the thesis of P.-E. Peterson [:ref:`bib1 <bib1>`]. This test is in fact one of the most frequent experimental references for validating models of surface or volume damage of concrete.

A beam of length :math:`2m`, height :math:`200\mathit{mm}` and thickness :math:`50\mathit{mm}`, notched in the middle on :math:`100\mathit{mm}` (half the height of the beam) is simply supported on its two ends.


.. image:: images/10000201000002C1000000F1E180B6898A12F132.png
    :width: 5.4882in
    :height: 1.8756in


.. _RefImage_10000201000002C1000000F1E180B6898A12F132.png:

Interface elements (60 QUAD4)

Figure 1: Representation of the 3-point bending beam. The thickness is :math:`50\mathit{mm}`


Material properties
----------------------


The law used is law CZM_EXP_MIX.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Material parameters are defined under the keywords RUPT_FRAG or RUPT_FRAG_FO

Young's module: :math:`E=30\mathit{GPa}`

Poisson's ratio :math:`\nu =0.2`


.. csv-table::

    "Critical surface energy density :math:`{G}_{c}`:", "GC= 137 N/m"
    "", ""
    "critical stress :math:`{\sigma }_{c}`:", "SIGM_C = 3.3 MPa"
    "", ""
    "Penalization of the Lagrangian", "PENA_LAGR =300"
    "", ""
    "Slip stiffness", "RIGI_GLIS =10 (by default)"



.. _RefHeading__31154616:


Boundary conditions and loads
-------------------------------------

**Embed**: The movements imposed following Oy are zero at the 2 support points (GROUP_NO: CL1 and CL2). We block the next 0x movement on one of the two supports.

**Displacement:** An imposed displacement following Oy is applied above the crack (GROUP_NO: Dpl).