What I understood is that you're trying to do a non linear static analysis whith forces as your imposed boundary conditions which doesn't converge any more when you reach the buckling point. To get the full force-displacement curve and see the post buckling behavior you either need to use displacements as an imposed boundary condition or an arch-length solver (this last one is called Ricks in Abaqus).

If you perform a static analysis for a post buckling analysis your assumptions are not valid any more. If you want to perform a post buckling analysis you have to do that as a transient analysis. In that case you model the real dynamics of your problem. The work around to stabilize the solution is to use a velocity dependend damping factor. In that case you have to run multiple simulations to be sure, that the damping does not effect the result. If you want to know more details you can ask a colleage of mine. She nearly finished her PhD about this topic

https://www.researchgate.net/profile/Regina_Khakimova?_sg=RArmCpbjj-jYUOyh6z-KSBJzAn3SGfq1DkYdmiZdZn0pGa2bZigAONxxB-UAB8QyDNxNpHb6rQzuq8wsWe5y-Q.cI0wJ34g7VMoYKs4eH-1-mIFkLN2Uja7TPNyAKxHD1y1TnhIj9zN3axeBnQGa9KP

Hi all,

Thanks for your answers.

Mr. Decelle: yes I am trying to get the post-buckling behaviour but my boundary conditions are actually specified in displacements, as you had suggested.  I'm not specifying a force as a load at all.  I'll check out Ricks in Abaqus. 

Mr. Willberg: would Abaqus Explicit be needed in this case?  Since it is intended for dynamics analysis? 

Hi,

I experienced the same problem, I believed that the problem is not the imperfection. Moreover, I realized that applying the imperfection on the geometry lead to more accurate results than the model with defined imperfection as displacement boundary condition. I think the problem is the time increments and the applied force, try with the smaller load and smaller time increment. Plus, try to apply a displacement boundary condition instead of load.

"would Abaqus Explicit be needed in this case?"

You can run it explict or implicit.

The advice of Zohreh Asaee won't help you in any case. The displacement boundary conditions reduce the size of the stiffness materix. Therefore, the system of equations are better solvable and the convergence problems may be stabilzed.

Also it depends what you want to model. A displacement boundary condition defines the movement of a point or multiple points. A load apllied somewhere influences localle the stress path, but the deformation in this area has to be solved.

Mr. Asaee: I am applying the imperfection to the geometry itself and not through the imperfection card/heading that can be added in the input file.  I got it to buckle many times this way but, as said before, it seems to be that it can't always get past the point of buckling.  The error I keep getting is "maximum attempts at this time step exceeded" (or however that normally is worded in abaqus).  

Mr. Willberg: The way that the system is being loaded in the experiments is through applying a displacement.  Thus, this is the way that this is being modelled for the post-buckling analysis here.  The resulting eiganvalues specify a multiplier on the buckling BC applied.

I've increased the maximum attempts at each time step by changing some solver options that are hidden in some menus throughout CAE

After further trial and error, I'm wondering if this is a mesh-related phenomenon...