# Do these linear vs nonlinear buckling plots make sense?

I am doing linear buckling analyses (where everything is linear), and nonlinear buckling analyses where you have nonlinear geometry enabled and nonlinear material behavior (hyperelastic material). Everything is done in COMSOL. The structure is fixed on one side, and a forced displacement of -0.01m in the x-direction on the opposite side. It seems the linear model buckles earlier compared to the nonlinear? What could be the reason for this, and does it look okay otherwise?

The blue lines are the nonlinear plots, and red/yellow dotted line endpoint is the buckling strain and stress - I have just made it into a line for easier visualization.

• I suggest providing a table to list the resulting stresses and strains for ease of comparison.
– r13
Jul 3 at 15:45
• If the geometry and loading are both "perfect" in the model there might be no reason for the nonlinear analysis to produce buckling. Your description seems to mean you are applying the load by controlling the displacements not the loads, in which case the nonlinear algorithm might by capable of tracking along an unstable branch of the structural response. Try running the nonlinear analysis with a small amount of transverse load (e.g. 1% or 0.1% of the axial load) and see if you get a different result. Jul 3 at 15:59
• @alephzero - you are right in that I control the displacement and not a load, I dont apply any loads at all actually, just the displacement, this isnt wrong is it since it still seems to buckle? Because I know buckling analyses requires some sort of perturbation to see which way the model will buckle, do we get this perturbation when we apply displacement to this model? Should I apply 1N in the transverse direction and see if I get the same stress/strain curve? Jul 3 at 17:30
• @r13 - the linear buckling stress and strain is just a point so its easy to provide in a table, but what about the nonlinear curve, its a bunch of points and im not sure at which part of the curve would be appropriate to say it has buckled? Jul 3 at 17:31
• Before you are getting comfortable with the program. I suggest performing studies on a simpler structure - a rectangular cantilever, with a constant cross-section length a = 10 mm, and thickness b varies from 0.5 mm to 4 mm. Then apply a compressive load equal to (pi^2)*E*I/L^2 for each case and see what happens. Note E & L are constant for all cases.
– r13
Jul 3 at 18:49