<CRITERION> nouailhas#
Description#
This criterion is a macroscopic model developed by ONERA for simulating anisotropic deformation of single crystals. The model does not accurately represent the individual slip system deformations, or their interactions, but could be useful for efficiently modeling the basic anisotropic behavior of a single crystal.
The criterion is written:
(364)#\[f_{cr} = \left\lbrace \left( \left[
\dfrac{3}{2}(a_1I'_1 + 2a_4I'_4)\right]^2 +
3a_8I'_8 \right)^3 -
(a_6I'_6)^4 \right\rbrace^{1/12} - R\]
(365)#\[\begin{split}\begin{aligned}
I'_1 &= S_{11}^2 + S_{22}^2 + S_{33}^2\\
I'_4 &= S_{12}^2 + S_{23}^2 + S_{31}^2\\
I'_6 &= S_{12}S_{23}S_{31} \\
I'_8 &= S_{12}^4 + S_{23}^4 + S_{31}^4\\
\end{aligned}\end{split}\]
with \(\ten S=\ten \sigma^\prime -\ten X^\prime\)
The criterion is associated:
(366)#\[\vect n = \pder{f}{I'_1}\pder{I'_1}{\ten \sigma} +
\pder{f}{I'_4}\pder{I'_4}{\ten \sigma} +
\pder{f}{I'_6}\pder{I'_6}{\ten \sigma} +
\pder{f}{I'_8}\pder{I'_8}{\ten \sigma}\]
This criterion is fully implemented, such that it will work with any
normal gen_evp or reduced_plastic potential, with any otherwise
valid integration. In 2D, the 23 and 31 terms are taken as zero.