**process tsai_wu_failure#

Description#

This post-processing computes the failure index using the Tsai-Wu failure criterion. The failure index is given by

(24)#\[\begin{split} \begin{aligned} &f_1 \sigma_1 + F_{11}\sigma_1^2+ F_{12}\sigma_1\sigma_2+ F_{13}\sigma_1\sigma_3 \\ &+f_2 \sigma_2 + F_{22}\sigma_2^2+ F_{12}\sigma_1\sigma_2+ F_{23}\sigma_2\sigma_3 \\ &+f_3 \sigma_3 + F_{33}\sigma_3^2+ F_{13}\sigma_1\sigma_3+ F_{23}\sigma_2\sigma_3 \\ &+F_{44}\sigma_4^2 \\ & + F_{55}\sigma_5^2 \\ & + F_{66}\sigma_6^2 \leq 1 \end{aligned}\end{split}\]

where \(f_i\) and \(F_{ij}\) are material coefficients, and \(\sigma_k=\{\sigma_{11},\sigma_{22},\sigma_{33},\sigma_{12},\sigma_{23},\sigma_{33}\}\).

The Tsai–Wu criterion predicts failure when the failure index reaches or exceeds 1.

Syntax#

**process tsai_wu_failure \(~\,\) *var var_name [ *output oname ]

where var_name is the stress tensor, and oname is the name of the failure index (Default TWU).

Outputs:

  • oname: the failure index.

  • oname_2: indicator function ( 1 if failure index \(>\) 1 else 0).

  • oname_3: step function (0 if index \(<\) 0.5, 0.5 if index \(\leq\) 1, else 1).

  • oname_C: breakdown of the contributing terms, grouped by stress components as in eq. (24). For example, if the value is 3, it means that the contributions from \(\sigma_{11}\), \(\sigma_{22}\), and \(\sigma_{33}\) together are still below 1, i.e. failure has not yet been triggered by these terms.

Example#

***local_post_processing
 **file integ
 **elset ALL_ELEMENT
 **material_file tsai.dat
 **process tsai_wu_failure
  *var sig

The coefficients \(f_i\) and \(F_{ij}\) should be given as

% tsai.dat
***post_processing_data
 **process tsai_wu_failure
   F11 1.489e-11
   F22 2.54e-9
   F66 4.238e-9
   F12 -9.72e-11
   f1 2.65e-6
   f2 9.13e-5
***return