Standardization of the refund rate G
======================================


2D plane stresses and plane deformations
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In dimension 2 (plane stresses and plane deformations), the crack bottom is reduced to one point and the value :math:`G(\theta )` from the CALC_G_XFEM command is independent of the choice of field :math:`\theta`:

     :math:`G=G(\theta )\forall \theta \in \Theta`


.. _Ref154550832:


Axisymmetry
-----------

In axisymmetry it is necessary to normalize the :math:`G(\theta )` value obtained with *Aster* for option CALC_G:

     :math:`G\mathrm{=}\frac{1}{R}G(\theta )`

where :math:`R` is the distance from the crack bottom to the axis of symmetry [:external:ref:`R7.02.01 §2.4.4 <R7.02.01 §2.4.4>`].

For option CALC_K_G, the values of :math:`G` and :math:`K` provided in the result table are directly the local values, so they should not be normalized.


Model symmetry
------------------

If we only model half of the solid in relation to the crack:


* or specify the keyword SYME =' OUI 'in the commands concerned;


*or do not forget to multiply by 2, the values of the energy recovery rate :math:`G` or :math:`G(s)` and by 4 those of :math:`{G}_{\mathrm{Irwin}}`*.* In addition, the values of the stress intensity factors corresponding to the mode of symmetry must also be multiplied by 2.