<POROUS_CRITERION> elliptic_aniso

Description

This porous potential allows for a very general anisotropic anisotropic porous plastic material. Anisotropic influence on the direct stress components for the (ordinarily) trace operator for the pressure term are replaced with a coefficient factored trace. Anisotropic effects in the shear term can be implemented with the generally available *shear_anisotropy option in the porous plastic material behavior (which replaces the \(J_2\) term with an effective anisotropic measure of the shear criterion).

The potential is therefore:

\[3C \tilde{J}_2^2 +F \tilde{I}_1^2 - \sigma_\star^2\]

where \(C\) and \(F\) are the coefficients named C and F, and which can depend notably on the porosity variable f. As stated above the \(\tilde{J}_2\) will be as supplied by the shear anisotropy (default standard \(J_2\) measure), and the \(\tilde{I}\) is calculated by:

\[\tilde{I}_1 = p\,\sigma_{11} + q\,\sigma_{22} + r\,\sigma_{33}\]

and \(p\) \(q\) and \(r\) are coefficients (not depending on state variables).

Syntax

The syntax follows the typical porous potential format with the 5 coefficients C, F, p, q, and r to be entered. Again, only C and F can depend on the porosity.

*porous_criterion elliptic \(~\,\) coefficients \(~\,\) …

Example

An example test is in Sam_test/INP in the input files elliptica and ellaniso.inp

  ***behavior porous_plastic
    **elasticity orthotropic
      y1111 464.
      y2222 239.
      y3333 239.
      y1212 105.
      y2323 105.
      y3131 105.
      y1122 172.
      y2233 142.
      y3311 172.
    **porous_potential
     *porous_criterion elliptic_aniso
       C 1.
       F          1.839926000000000e-03
       p 1.
       q          2.061266000000000e+01
       r          2.330418000000000e+01
     *shear_anisotropy hill
       hilla          4.172356995000000e-01
       hillb          2.066054000000000e+00
       hillc          1.992586000000000e+00
       hilld 1.
       hillf 1.
       hille 1.
     *flow norton    % pseudo rate independant
       K 0.001 n 10. % plasticity with these coefs
     *isotropic_hardening nonlinear_double
       R0          4.500000000000000e-01
       Q1          3.729991000000000e-01
       b1          3.276424000000000e+02
       Q2          8.166423000000000e+03
       b2 0.001
***return