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5 June 2016

# How to set up materially nonlinear analysis

In this post, I will show you how to define and run a materially nonlinear analysis in a video tutorial. This is the type of analysis that will allow you to calculate a plastic collapse load of the model. This is one of the important parameters in the numerical design.

Plastic collapse is one of the possible ways the structure we are analyzing can fail. Sometimes this criterion is simply met by limiting the stress to the yield stress in the entire model – this way a linear analysis (LA) is sufficient in design since when everywhere stress is below yield there is no need for materially nonlinear design (of course this not include hyperelastic materials etc.). However, such an approach is quite limiting, since in most cases there will be stress concentrations in various places, and to reduce the stress in so-called “hot spots” to values under yield stress requires a usually great thickness of elements. Also, the fact that some parts of the model yielded does not mean that the capacity is exceeded. After all Eurocodes (European norms for civil engineering) simply allows for plastic design, which in certain situations leads to yielding of an entire cross-section of the analyzed beam.

With this in mind, it is actually beneficial to perform a Materially Nonlinear Analysis (MNA) to verify what is the actual capacity of the model due to plastic failure. One should be aware however that in certain situations using plastic capacity might not be the best idea. This is especially true when fatigue is an issue (with periodically changing loads) since yielding leads to such problems as low-cycle fatigue, characterized by much smaller fatigue resistance. Also if the plastic capacity of the model is close to the elastic capacity due to instability then there is an interaction between those 2 effects further reducing the global capacity of the model. This is why not only do you have to analyze plastic and elastic capacity (elastic capacity needs to be verified with proper imperfections), but also you wish to verify both nonlinearities at the same time to check, whether they interact with each other.

Verifying plastic capacity without a stability path is actually quite difficult because looking at the yield zones in the model under various loads it is hard to decide how big a yield zone we can allow. I described this more here. In today’s example yielded zones in the model under increasing loads would look like this:

As you can see it is not easy to decide at which stage the yielded zone is too big and when the model lost capacity. This is, however, a problem for the next post – for now, let’s focus on how to actually perform an analysis that allows us to obtain such results.

In the video tutorial below I explained the most important aspects of MNA calculations on the shell example using Femap with NX Nastran. Please note, that the solver parameters were discussed previously here.

I hope you enjoy this tutorial and find it useful. If you have any questions post them in the comments below.

Have a good one

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#### Author:Łukasz Skotny Ph.D.

I have over 10 years of practical FEA experience (I'm running my own Engineering Consultancy), and I've been an academic teacher for a decade. Here, I gladly share my engineering knowledge through courses, and on the blog!

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### Join the discussion

Sultan - 2020-11-15 20:43:06

Hello! Quick question, I am trying to run a nonlinear analysis for a latex skin, which is nonlinear and has no defined youngs modulus, so how would I go about defining that material in femap?

Regards,
S

Łukasz Skotny Ph.D. - 2020-11-16 16:47:20

Well... it seems that latex skin has a pretty awesome material model. First of all, you need to know what that model is (you know stress-strain relationship and all other considerations latex may have) only knowing that it makes sense to discuss how to approach such material in Femap...

Simply put I know too little about latex to be of any help here!

All the best!
Ł

Hi, thank you for your pist n simple explanations given in this blog.

Appreciate if you can share the details of setting up a material nonlinearity analysis with a case where 3 out of 4 loads in the model to be constant and will only need to vary the fourth load.. can we do this in Femap?

Łukasz Skotny Ph.D. - 2018-04-13 06:31:17

Hey!

I have never done that, to be honest... but I think you can do this with initial conditions.
Normally I would say that I will "look into it" but I have so many things on my plate right now, that I don't have the capacity to run tests right now for you.

I really hope you will find what you need! (also try dealing with that in subcases... you can add 3 the same loads and one different... so it should iterate to that state nicely) - that would require testing to check if it would work!

All the best
Ł

Werner Bramlette - 2016-11-06 16:41:56

Awesome blog, going to bookmark it!

Łukasz Skotny Ph.D. - 2016-11-06 17:04:28

I'm glad you like it :)
See you around! If you have any questions regarding FEA do not hasitate to write to me - I will try to help out :)

Cheers
Łukasz

Mathias - 2016-06-17 15:51:06

Hi Lukasz, again very good tutorial!

Small question:
Before reaching the yelding strength of the material, the software uses the modulus of elasticity to get the linear displacement of the structure. But how does it interpret the displacement after reaching the yielding strength? Is there a kind of a 'after yield' curve implemented in the software?

Have a nice weekend!

Łukasz Skotny Ph.D. - 2016-06-18 16:37:53

Hi Mathias,

Yes, there is an "after yield" curve. Actually there are many models of yielding you can use - in this case I have used a "plastic" model which means that after reaching yield the line on the stress-strain chart is horizontal.