**process maximal_stress_failure#

Description#

This post-processing computes the failure index using the Maximum Stress Failure criterion. Material safety requires that the stress components satisfy

(23)#\[\begin{split}\begin{aligned} \frac{\sigma_1}{\tt \sigma_{11 t}} \leq 1 ~ \text{if} ~ \sigma_1 \geq 0 &\quad \text{or}\quad \frac{\left|\sigma_1\right|}{\tt \sigma_{11 c}} \leq 1 ~ \text{if}~\sigma_1<0\\ \frac{\sigma_2}{\tt \sigma_{22 t}} \leq 1 ~ \text{if} ~ \sigma_2 \geq 0 &\quad \text{or}\quad \frac{\left|\sigma_2\right|}{\tt \sigma_{22 c}} \leq 1 ~ \text{if} ~ \sigma_2<0\\ \frac{\sigma_3}{\tt \sigma_{33 t}} \leq 1 ~ \text{if} ~ \sigma_3 \geq 0 &\quad \text{or}\quad \frac{\left|\sigma_3\right|}{\tt \sigma_{33 c}} \leq 1 ~ \text{if} ~ \sigma_3<0\\ \frac{\left|\sigma_4\right|}{\tt \sigma_{44}} & \leq 1 \\ \frac{\left|\sigma_5\right|}{\tt\sigma_{55}} & \leq 1 \\ \frac{\left|\sigma_6\right|}{\tt\sigma_{66}} & \leq 1 \end{aligned}\end{split}\]

where \(\sigma_k=\{\sigma_{11},\sigma_{22},\sigma_{33},\sigma_{12},\sigma_{23},\sigma_{33}\}\).

The tensile and compressive strengths along the i-th direction are denoted by \(\tt\sigma_{ii t}\) and \(\tt\sigma_{ii c}\) respectively. The shear strengths are denoted by \(\tt\sigma_{jj}\), \(j=\{4,5,6\}\).

When any of the above equations exceeds 1, failure is predicted.

Note

This post-processing can also be used for the maximum strain failure criterion by substituting strains in place of stresses.

Syntax#

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

where var_name is the stress tensor (or strain in case of the maximum strain failure criterion) variable, and oname is the name of the failure index (Default MSC).

Outputs:

  • oname: the failure index (the maximum value of ratios in (23)).

  • 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: the failure mode. For example, if the value is 3, it means that the failure mode is identified with the failure surface associated with the action plane of \(\sigma_{33}\) and tensile direction (\(-3\) for compressive \(\sigma_{33}\)).

Example#

***local_post_processing
 **file integ
 **elset ALL_ELEMENT
 **material_file msf.mat
 **process maximal_stress_failure
  *var sig

Material coefficients are given as

% msf.mat
***post_processing_data
 **process maximal_stress_failure
   sigma_11_t 1700.
   sigma_11_c 1150.
   sigma_22_t 63.
   sigma_22_c 180.
   sigma_33_t 63.
   sigma_33_c 180.
   sigma_44 72.
   sigma_55 72.
   sigma_66 72.
***return