Another (maybe remote) possibility is that physically (during testing), multiple side-by-side columns of the porous structure (such as the one represented with your 1/4 symmetry model) deflect laterally as a group when the structure is compressed (with each individual column deforming in much the same way beam buckling is depicted in engineering textbooks (Buckling - Wikipedia):
With symmetry models, we usually constrain the normal component of displacement on the symmetry surfaces. You didn't mention doing this yourself, but if you did, that would prevent the model from exhibiting the deformation mode that I'm describing.
I am a little confused by the image of your model (which appears to be 1/4 symmetry of the geometry of a single "column") and your reference to "1/14 symmetry" - I may be missing something that renders my discussion inapplicable.
Is the model that Mechanical creates for you meshed with SOLID285?:
Given your use of an Ogden material model, I suspect this is the case, but if not, these do tend to be less susceptible to mesh entanglement problems such as the one you're experiencing.