Convergence test of FEA model.

[Orthohass]

I am inteterested in the peak values of stress and strain in a model.
My question is about how to check the reliability of the model through convergence test.
If I am interested in the peak value of maximum principal strain, should I check the convergence behaviour of this parameter when mesh is refined. Or if the global strain energy converged, that woud be enough evidence that the model is reliable one.
What if strain diverged? What it might mean? All the threads I check on internet about singularity prooblem, relate this problem to stress. Can strain also present singularity problem.

 

[rb1957]

if you have a particular parameter in mind, i guess it's best for track convergence of this; but it shouldn't matter much.

this convergence test means that further refinements in the mseh don't change the results. it makes sense (to me at least) to refine the mesh in places with a high stress/strain gradient. as you refine the mesh you should see the peak values increasing, hopefully at a decreasing rate with each remesh, and it "should" converge on a number.

looking at global parameters probably won't tell you much. if you're looking at stress peaks, the global strain energy won't change much.

another day in paradise, or is paradise one day closer ?

 

[IceBreakerSours]

The focus of your (spatial) mesh convergence study - at a location of interest - should be your specific field variable of interest.

Strain (and, therefore, stress) singularity occurs at crack tips, as an example. While I have not conducted a study and I *feel* rb1957 might be correct in saying that "..it shouldn't matter much..", I am not entirely sure and here's why: In a typical structural analysis, displacement is the primary variable, whereas strain is a derived variable and stress comes from the constitutive law + the strains. I *think* just because one field variable has converged should not necessarily guarantee convergence for a derived variable at that location. This suggests a clear hypothesis and something you should try and learn for yourself (and report back)

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[Reitzel]

As a rule of thumb the element mesh should be fine enough to obtain convergence on global load-deflection curves. For most cases it is impossible to obtain convergence with respect to strain development.

 

[Orthohass]

Thank you all.
Reitzel, would you please explain more why Strain would not converge in most caese. My research significant findings were based on strain parameters. I think that if want to prove the relibilty of my findings, I should prove that these parameters converge. I have just found that peak maximum principal starin although converged but with some oscillation. Peak minimum pricipal strain never converged. Stress parameters converged very well, but actually they are not my interest. I am more interested in strain parameters.

 

[Reitzel]

Dear Orthohass
I'm afraid that I can't give you a mathematical or physical explanation within the FEM framework. My statement is based on my experience with the FEM.

 

[rb1957]

i'd've thought that strain should converge better than stress, which is derived from an initial strain assumption (99% of elements are formulated on an assumed strain distribution, and stress is dervied from this).

it's odd for max principal anything should converge whilst min principal doesn't.

but be careful about chasing FE results all the way into a stress concentraion ... the results are really not valid (unless you're running non-linear).

another day in paradise, or is paradise one day closer ?