Problem in nonlinear analysis - boundary conditions

[Zem]

I am trying to run nonlinear analysis in Abaqus under uniform traction boundary conditions. I need to find the maximum extension I can get using Abaqus for this type of problem.

I found that Abaqus can handle this problem till some specific value of the pressure magnitude and then the analysis fails. It is a simple homogeneous rectangular plate, made of neo-hookean type material, subjected to loads from both sides and constrained from rigid body motion on the corners (plane stress). I tried almost everything: using controls, defining other types of boundary conditions, adjusting increment step – nothing works. Under displacement boundary condition there is no limit – analysis completes successfully for any displacement applied, whereas under traction boundary condition the maximum extension I can get is around 1% of the plate size, which is unacceptable for my research.

Is there any bug Abaqus has for nonlinear problems of this type? Has someone tried to apply this type of boundary conditions in nonlinear analysis?

 

[corus]

Under a displacement condition the solution is strain dependent, and hence will solve. For an applied load with perfectly plastic material you may have infinite strain and thus no solution. If that's the case then try putting in a slight slope in your stress-strain material properties.

corus

 

[feadude]

If this was a plate bending problem, it will give you higher displacement when solving. However for plane stress problem if the stress strain curve has an area of zero slope, then if the flat portion is substituted with a slight strain hardening, it might solve.

 

[Zem]

Thanks for the reply. The thing is that I am not considering plasticity - it is a purely elastic problem.

 

[corus]

Then it must have buckled.

corus

 

[Zem]

I didn't think about buckling problem, although Abaqus always reports negative eigenvalues. You must be right. But the plate is not under compressive loads - it is stretched. I have never heard about buckling of a stretched plate. Can that happen?
Thank you.

 

[feadude]

No a plate under tension can not buckle.

 

[corus]

If you take a piece of polythene with a hole in it and stretch it then it appears to buckle at the hole, due to compressive stresses being present at the hole.

corus

 

[feadude]

zem:

Is there a hole in your rectangular plate?

 

[pja]

What does fails mean? Does it not converge? Are you getting small pivot messages? Have you tried refining the mesh to see if that helps? I'm not familiar with the nonlinear solver in Abaqus..is the geometric nonlinearity handled with a co-rotational formulation? If so maybe try an element which uses an updated Lagragian formulation. I've had better luck getting models with large displacements and rotations to converge with this type of formulation. In order for you to get more help you need to explain what you are doing and what problems you are having better.

 

[Zem]

Thank you very much for all your replies.

I don't have any holes or cracks in my plate. Initially, I tried to run analysis for heterogeneous plate - it didn't work. Then I started to simplify my model and finally came to a simple homogeneous plate under uniaxial tension. I should say that plate is constrained only on its corners and not on its edges.

Fails means analysis doesn't converge. I tried to refine mesh, but it didn't give anything. Program always reports negative eigenvalues and after sometime analysis fails.
As far as I know all stress/diplacement elements in Abaqus are based on Lagrangian description.

 

[corus]

Is the plate rectangular?

corus

 

[Zem]

Yes, it is rectangular.

 

[ThomasH]

Since I don't use ABAQUS I can be completely wrong in this matter, but.

You mentioned negative eigenvalues and plate in tension. Since eigenvalues are typically associated with buckling and compression I would say that the negative sign is ok. (For the moment I'll ignore dynamics.)

Can you make a linear analysis work and check the stressdistribution? That might give a hint as to why nonlinear fails. Also, you say "pure elastic". Why run nonlinear at all?

Good Luck

Thomas

 

[corus]

I think negative eigevalues also refers to a general non-convergence of a problem rather than buckling. In the original posting it sasy that the load is applied at both sides. My guess is that restraints haven't been provided correctly so no solution can be found. For a simple rectngular plate use symmetry conditions and restrain one edge and only apply the load to one side of the plate.

Incidentally, how can the material be non-hookean and yet be purely elastic?

corus

 

[Zem]

There are two reasons I am running nonlinear analysis:
1) I am interested in large deformations, therefore nonlinear analysis should be on and
2)I am interested in constitutive response of an inhomogeneous plate (neo-hookean material models hyperelastic material response)
Because of the second reason I cannot use symmetry condition, although now I am considering a homogeneous case. I, actually, tried to use symmetry - force can be increased till certain level but then analysis fails again.
I tried linear analysis - it always works and creates homogeneous stress destribution inside the plate.
Also, if I have restrained the plate incorectly, analysis would fail even for small pressure magnitude which doesn't happen.

 

[pja]

As you've said you've tried to refine already the only thing I can tell you is to try and apply the load in smaller increments ..with ANSYS you can apply the load in steps during a static solution..perhaps this can be done with Abaqus as well.

 

[var81]

I am also facing similiar problem.But only difference is i am using symmetry BC and rectangular plate has holes .I tried mesh convergence that didn't help me.