4. Standardization of the refund rate G

4.1. 2D plane stresses and plane deformations

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

\(G=G(\theta )\forall \theta \in \Theta\)

4.2. Axisymmetry

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

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

where \(R\) is the distance from the crack bottom to the axis of symmetry [R7.02.01 §2.4.4].

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

4.3. 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.