<CRITERION> modified_nouailhas#
Description#
This criterion modifies the nouailhas model above by basing the
calculation of the \(I\)’s on the actual tensors
\(\ten \sigma -\ten X\) in place of the deviator, and includes an extra
term:
(362)#\[f_{cr} = \left\lbrace \left( \left[
\dfrac{3}{2}(a_1I_1 + 2a_2I_2 + 2a_4I_4)\right]^2 +
3a_8I_8 \right)^3 -
(a_6I_6)^4 \right\rbrace^{1/12} - R\]
(363)#\[\begin{split}\begin{aligned}
I_1 &= S_{11}^2 + S_{22}^2 + S_{33}^2 \\
I_2 &= S_{11}S_{22} + S_{22}S_{33} + S_{33}S_{11} \\
I_4 &= S_{12}^2 + S_{23}^2 + S_{31}^2 \\
I_6 &= S_{12}S_{23}S_{31} \\
I_8 &= S_{12}^4 + S_{23}^4 + S_{31}^4
\end{aligned}\end{split}\]
with \(\ten S=\ten \sigma -\ten X\)
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.