I have found the following example which is produced as documentation for RS3 geotechnical FE software. This is a validation document that goes through an analytical verification of triaxial testing for modified cam clay material model. It relies heavily upon the p-q stress representation of the model to make its argument.
I find it to be quite pedagogical in the way it presents its content. It has enabled me to somewhat understand the following diagram:
For this example triaxial test the isotropic stresses are initialized at point $(p,q) =(p_i, q_i)=(200,0)$. The deviatoric stress $q$ is then applied until the sample 'fails'. This is the intersection between the green line and the red line (CSL).
This means that for a given axisymmetric FE analysis with following boundary conditions:
It is only possible to generate ONE p-q green dashed line.
I would like to know if there is a way to plot the ENTIRE surface. This would perhaps imply that I would have to force the sample to take several different stress paths and have them each intersect with the ellipse? Computational efficiency is not really the issue here, it is more the method. How do I force the sample to take different stress paths such that I can plot the entire yield surface? Is this even possible? Am I even asking the right question?