`**process coppola`#

Description#

This post-processing computes the damage by integrating the equation, proposed by [U10],

(14)#\[D = \int_0^{\varepsilon_f} \dfrac{C_1}{g(\theta)^{1/n}} \exp (C_2T) d\varepsilon^p\]

where

\(C_1\), \(C_2\), and \(n\) are material parameters,
\(\theta\) is the Lode angle,
\(T\) is the triaxiality parameter (the ratio of the hydrostatic stress to the von Mises stress),
\(\varepsilon_f\) is the equivalent plastic strain at fracture, and \(\varepsilon^p\) is the equivalent plastic strain.

The function \(g(\theta)\) is given by

\[g(\theta)=\frac{\alpha}{\cos \left[\frac{\pi}{6}\beta-\frac{1}{3} \cos ^{-1}(\gamma \cos 3 \theta)\right]}\]

where \(\alpha\), \(\beta\), and \(\gamma\) are material parameters. The eq. (14) is integrated numerically using the trapezoidal rule.

**process coppola [ *stress stress ] [ *strain strain ]

*stress stress: name of the stress tensor (Default sig).
*strain strain: name of the equivalent plastic strain (Default epcum).

The name of the output damage variable is Er_coppola.

***local_post_processing
 **file integ
 **elset ALL_ELEMENT
 **material_file coppola.mat
 **process coppola

The material coefficients should be given as

% coppola.mat
***post_processing_data
 **process coppola
   C1 0.05
   C2 0.1
   n 5.
   alpha 0.007
   beta 2.6
   gamma 0.32
***return