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


Geometry
---------

A domain of length :math:`l=\mathrm{6000mm}`, height :math:`h=\mathrm{1000mm}` containing an initial vertical crack of length :math:`\mathrm{2a}` is represented. By symmetry condition, only half of the domain () is modelled.


.. image:: images/Object_18.svg
    :width: 445
    :height: 143


.. _RefImage_Object_18.svg:

Illustration 1: Geometry of the test case


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

**Elasticity parameters:**

Young's modulus :math:`{E}_{1}={20.10}^{9}\mathrm{MPa}`, Poisson's ratio :math:`{\nu }_{1}=\mathrm{0,25}`

**Law settings** ENDO_HETEROGENE **:**

Elastic limit :math:`{\sigma }_{y}={10}^{18}\mathrm{Pa}`

Weibull module :math:`m=2`

Tenacity :math:`{K}_{c}=1000{\mathrm{MPa.m}}^{1/2}`

Thickness of sample :math:`\mathrm{ep}=\mathrm{1m}`

Seed :math:`\mathrm{GR}=121`

**Non-local model parameter:**

Characteristic length :math:`{l}_{c}=\mathrm{0,02}m`


Boundary conditions and loading
------------------------------------

Vertical movements on the lower edge of the model are blocked as well as horizontal movements on the left edge and a horizontal constraint is imposed on the right edge. The central crack is represented by a vertical band of broken finite elements (*i.e.,* :math:`d=1`).

The stress applied on the right edge varies from 0 to :math:`10\mathit{MPa}` during the calculation period, i.e. :math:`1s`.


.. image:: images/Object_12.svg
    :width: 445
    :height: 143


.. _RefImage_Object_12.svg:

Figure 2: Diagram of boundary conditions