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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

The structure studied is a :math:`375\mathrm{mm}` long bar. Since the problem is purely :math:`\mathrm{1D}`, his section has no influence.


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

In modeling A, the material obeys a law of fragile elastic behavior (ENDO_SCALAIRE) with a damage gradient (modeling *_ GRAD_VARI).


.. csv-table::

    "ELAS "," ENDO_SCALAIRE "," NON_LOCAL"
    "E= :math:`30000\mathrm{MPa}`
    NAKED = :math:`0` ", "SY= :math:`3\mathrm{MPa}`
    GAMMA = :math:`4` ", "C_ GRAD_VARI = :math:`1.875N`
    PENA_LAGR = :math:`1.5`"


In modeling B, the material obeys a law ENDO_FISS_EXP for which the following parameters are entered: E = 30,000 Mpa, NU = 0, ft = 3 MPa, fc=30 MPa (without affecting the 1D result), Gf=0.1 N/mm, p=1.5, D=50 mm (without affecting the 1D result), Gf=0.1 N/mm, p=1.5, D=50 mm.


Loading conditions
------------------------

The left part of the bar (:math:`125\mathrm{mm}` long) is forced to remain rigid (blocking the degrees of freedom of movement). As for the right part of the bar, it is subject to a uniform axial deformation :math:`{\varepsilon }_{0}`, that is to say to an imposed displacement whose spatial distribution is linear. A single parameter therefore controls the intensity of the load: the level of deformation imposed :math:`{\varepsilon }_{0}`.

In the directions perpendicular to the axis of the bar, the movements are blocked: the problem is purely :math:`\mathrm{1D}`. Furthermore, as the Poisson's ratio is zero, no clamping stress develops in these directions.