What happens when you unload the test structure? Does it permanently deform, after buckling, or does it spring back to its original shape? If there is local damage (or yielding) occurring in the resin, the hyperelastic material model is not going to capture that. Perhaps a Three Network Model would be a better material option. If it is purely hyperelastic, with no local damage, perhaps the 1st order Ogden is just insufficient to fully capture the stiffness response in the 3D stress state. If that is the case, can you generate material test data in tension, shear and compression; and curve fit this to a higher order Ogden model?
Also, what about self-contact between the surfaces on the interior of the structure? Do the surfaces remain separated, or do they collapse onto each other? If there is nonlinear contact between internal surfaces, perhaps that explains the sharp increase in stiffness response at larger strains.
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