**process beremin#

Description#

This command performs the Weibull stress and the rupture probability according to the Beremin model [U12]. The Weibull stress is defined as:

\[\sigma_W = \left( \frac{1}{V_0}\int_{V,\, p>p_c} \sigma_I^m\,dV\right)^{1/m}\]

where \(V_0\), \(p_c\) and \(m\) are material parameters. \(\sigma_I\) is the maximum principle stress. The integral is taken over the volume where the plastic strain is higher than a critical value \(p_c\). The failure probability \(P_R\) is given by:

\[P_R = 1 -\exp\left(-\left(\frac{\sigma_W}{\sigma_u}\right)^m\right) = 1 -\exp\left(-\frac{1}{V_0}\int_{V,\, p>p_c} \left(\frac{\sigma_I}{\sigma_u}\right)^m\, dV\right)\]

\(\sigma_u\) is a material parameter.

Syntax#

**process beremin \(~\,\) *stress name1 \(~\,\) *strain name2 [ *fvol fv ] [ *scalar ]

*stress name1

is the name of the stress tensor

*strain name2

the name of the inelastic deformation measure (scalar).

*fvol fv

volume fraction correction. By default 1.

*scalar

this will consider only the first component of stress tensor.

Note

The material file must contain the values \(V_0\), \(p_c\) \(m\) and \(\sigma_u\).

Example#

****post_processing
 ***global_post_processing
  **file integ
  **elset ALL_ELEMENT
  **material_file a.mat
  **process beremin
     *stress sig
     *strain epcum
     *fvol 4.
 ****return

where

% material file a.mat
**process beremin
  V0      10.
  m       20.
  sigma_u 1200.
  p_c     0.01