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8 minutes read
14 November 2017

Design for stress, strain or rigidity?

8 minutes read

This topic was on my mind (and on my to-write list) for a very long time. Finally, I had the time to organize what I want to write about it in my head. I wonder what is your take on this matter – be sure to leave a comment below!

What does it mean to design something?

What I really like about FEA is the fact that it is a tool. It’s not a crystal ball that simply grants answers, and to be honest, I think this is what makes it so great!

When you will run an analysis you will get outcomes, and it’s only up to you to decide what you will do with them.

It’s obvious that you need to post-process results… the question is – what does it mean?

It all starts with stress!

I think that whether you are a beginner or an expert you will check stress levels in your model. This is the “obvious” thing to do. Stress nicely shows how much “hurt” your model is taking – something you definitely want to know : )

Typical checks then simply mean that you will plot the “von Mises” stress and check how big stresses are there. This may look something like that:

While checking equivalent von Mises stress is great, there are other things worth doing. One of them is checking different stress components. While equivalent stress nicely shows the overall “hurt” your model is taking, stress components will show you what is going on.

I think it is good to think about it like that: what happens in the model is a rather complex thing. It’s impossible to describe it with just one number. This means that whatever von Misses stress does it must “loose” a lot of information along the way to produce this one number.

This is absolutely true, as you can’t even tell if the stress comes from shear or from bending… nor can you tell if your model is in tension or in compression! This is why when you check stresses it is best to use a bit more than simple “von Mises” approach : )

Stress design ups and downs

The thing with stress design is, it works really great until yielding starts. Then depending on the analysis 2 things can happen:

  • If you are using linear analysis you will get stresses that are much higher than yield and doesn’t have real “physical” sense. You can read more here.
  • If you are using materially nonlinear analysis after yield stress remains almost constant (or simply constant) depending on the material model. This means that it is actually hard to draw conclusions from it when the “red zone” gets bigger and bigger.

This is why using stress as an indicator of “hurt” to the model works, but usually in models that don’t have stresses higher than yield. In such cases, answers are obvious without any doubt.

However when you go into “higher stress” models where yielding can happen things are getting more and more tricky.

What to remember about stress design:

  • Checking more than “von Mises” stress makes sense. Equivalent (von Misses) stress is great, as it shows the overall “hurt”, but seeing different stress components (like normal stress in direction X) tell you what is going on in the model.
  • Don’t guess based on the “red zones”! If you have stresses higher than yield it will be hard to make conclusions about capacity here. There are other ways of dealing with this 🙂

Strain is your friend : )

This is something I struggled to catch for years! It seems such a logical step, but somehow I missed it… I was doing stress analysis and I checked plastic collapse, but somehow I did not check plastic strain values. I started doing this some time ago, and now I feel much more confident : )

As I mentioned above, using linear stress analysis will leave you guessing about what is really happening in your model in stress analysis. However, when you go with nonlinear analysis the answer is not clear either…

… unless you check plastic strains. You see when material yields the stress remains more or less constant for a time. However, the plastic strain constantly increases.

This means, that when the stress becomes constant in an area (because of yielding), you can simply check strain to check “where you are”. There are even codes (like DNV-RP-C208) that states how much strain is allowable in different scenarios or in different conditions. This makes it super easy to use in materially nonlinear analysis.

Is strain design “a thing”?

I’ve read someone’s opinion, that inexperienced users use stress while experienced users use strain in design. I’m not sure if this is true (what do you think?) but “getting this” definitely changed what I understood.

I think that using strain in design was one of the major steps in my career when it comes to FEA. Somehow it made me “click” in few places at once and I understood a lot of things better. Have you read my post on how material nonlinearity works? One of the examples I used there came to me thanks to this realization.

I hope this will help you to get there faster if you haven’t used strain in design before!

Thing to remember about strain design:

  • Strain helps if you can’t read outocmes from stress! In case of materially nonlinear analysis, checking plastic strain will give you all information you need on where you are on the capacity curve of your material! Just establish a limit strain you will accept and you are good to go. Just don’t forget to check mesh convergence if necessary!
  • Strain is not all there is! While strain is a great indicator of what is going on in the material, don’t forget to check if stability of the model is ok. Even if elastic buckling was not an issue, plastic buckling can happen. This is because after yielding deformations are in a certain sense “free” in region that yielded. This naturally make buckling easier as you can see below. Be aware that even if strains are small, yielding can still cause a plastic collapse, and you need to check that separately!

Finally, the rigidity!

This is a topic that is a bit separate from the other two I think. But it doesn’t mean it is unimportant!

As I finished civil engineering it is easy for me to see that things not only have not to break but also should not deform all that much. In almost all civil engineering codes there are requirements about allowable deformation of different parts of the structure.

I would say this aspect is the first part of rigidity design. You just plot the deformations of your model, and then you check if you are ok with them. Usually, you will know what is “allowable”. Either by experience, customer expectations or simply code requirements deformations tend to be nicely defined. Sure there are exceptions, but as a general rule, I would say this is accurate.

There is always the second side of the coin

This is however only the first part. If the deformations are “high” you will catch everything you need with this. But when they are small there is another issue.

The rigidity of different elements influences how the load is distributed in the model (gummy bears anyone?). If the total deformations are high you will notice what is working and what deflects too much. You will actually “act” to fulfill the criteria.

When the deformations are small this requires effort to notice. Simply because all deformations are acceptable!

One could even say “why should I bother?”, and this is a justified question! If stress levels are ok, deformations are acceptable and there is no unacceptable strain, then this is a good design. In such a case, you can simply ignore this part… unless you want to optimize the element.

If there is a piece that is substantially less rigid than others it will take much less load. The question here is “should I fix this”? You can either remove the less rigid element or strengthen it to get the maximum from it. One of the two will most likely optimize the solution.

Of course, there are elements that are simply “necessary as they are”, but luckily many can be optimized this way : )

Gathering this all up

I would say all the methods I have described are needed. Often people refer to their job as to “stress design”, but obviously there is more to it. I think it is a good idea to mention strains and rigidity from time to time, simply to make everyone aware of this.

I know I needed such a post some time ago : )

Let me know what do you think about this matter, and which things you check yourself in the comments below : )

Want to learn more?

Post-processing isn’t as easy as it looks I would say. There is always something new to learn, and I hope you have learned something here. If you want to learn even more about FEA, you can learn some useful things in my free FEA course. You can get it below.

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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    Comments (20)

    Nikhil - 2023-11-29 07:04:15

    Hi Lukasz,

    Thanks for posting a very nice blog!

    I have two question :

    Question 1: If we get a very very high value of Eulers Eigen value buckling load multiplier (say a value above 20). Than I think the structure will be safe for buckling failure. As per ASME code, we need to fulfill only 1 requirement that is either Type 1 or Type 2 or Type 3 buckling.
    But you mention ''Even if elastic buckling was not an issue, plastic buckling can happen.'' How?

    Question 2: If we get convergence and a very small value of plastic strain (less than 0.02) than how plastic collapse can happen?
    Here, by 'plastic collapse' did you mean to say buckling failure?

    Łukasz Skotny Ph.D. - 2023-12-14 09:36:42

    Those are very good questions Nikhil!

    Funny enough - both have the same answer :)

    Imagine a situation where you have a shell structure (this is the easiest thing to use as an example). Such shells always buckle to the inside, simply because they don't have to increase the circumference to do so (and buckling to the outside would require increase of circumference, so it would be associated with generating high circumferential tension (so it's more difficult).

    BUT... if you yield a substantial area of the shell (and the "degree" to which you yield it is irrelevant, the plastic strains can be very low, as long as you are on a plastic plateau) suddenly the increase of circumference is not a problem anymore (on plastic plateau, you get strains "for free" without increasing stress, so the shell can simply elongate to increase the circumference). In such a state shell can just as easily buckle to the outside (usually there is an inside pressure of some sort, helping with that while preventing buckling to the inside, and outside buckling - called elephant foot buckling - doesn't happen because the increase of circumference is so difficult that it is still easier for the shell to buckle to the inside, even if the load opposes it). But as I said, if the shell yields, increase of the circumference is "free" and suddenly everything changes!

    So to answer your questions:

    1. LBA is linear, it will not see that the material yielded, and that something bad may be assosiated with this. It will always try to buckle the shell to the inside (although I know that the shapes are in both directions in LBA... this is a different story). So you simply can't check plastic collapse (aka elephant foot buckling) in LBA - regardless of how high the multiplier is.

    2. The elephant foot buckling doesn't require "high" plastic strains - it just requires that the material starts to yield, to get the "free strain increase without stress increase" - so it can easily happen in low strain values as well. And if you do MNA (nonlinear material, linear geometry analysis) you will not find this either, as this is a geometrical instability phenomenon, so it requires a nonlinear geometry in analysis to manifest.

    Hope this answers your question :)

    All the best!

    Mohamed Salih - 2023-03-25 10:36:03

    Hi Lukasz,
    As usual, your blog posts never fail to evoke some fundamental questions. Like stress and strain: which is the cause, and which the effect? Like the classical question which still remains unanswered: chicken or egg? Which came first?
    Probably belong to the philosophy of ‘Advaitha’ (non-duality) or dialectical materialism.
    Thank you for the engaging posts with your characteristic style of presenting mundane ideas in a philosophical manner. Not to mention the freshness of your handmade sketches!
    Look forward for more pearls of wisdom from the depths of structural mechanics.
    Best regards.

    Łukasz Skotny Ph.D. - 2023-03-27 09:05:52

    Hey Mate!

    I'm not sure if I can be as philosophical to post something smart here :P But I'm glad that you like the post ;)

    All the best!

    Nick Minehan - 2019-09-10 15:48:00

    Hi Lukasz,

    Can you use strain as an acceptance criteria for linear analysis past yield for an FEA study as the stress values are no longer accurate? Eg. if the strain is smaller than the strain at UTS then the part is not likely to fail? But then again the displacement is contingent upon the elastic modulus which is no longer valid past yield, therefore nonlinear FEA is required? I would greatly appreciate if you could clarity!!

    Łukasz Skotny Ph.D. - 2019-09-10 17:20:05

    Hey Nick!

    Sadly this won't work. I even do a case-study in my Breakthrough FEA course about this. You will get linear strain that is just as wrong as linear stress "post yield".

    You will need nonlinear FEA - but you know - learning that gives you power!

    All the best

    Niels - 2019-08-29 06:39:10

    Hi Łukasz,

    Won't the stress, or perhaps more accurately stress UR distribution indicate the same issue as the more advanced rigidity check? That is low stress UR in an element indicates potential optimization? Or is this more a optimization due to redistribution of stiffness which won't necessarily be obvious from the stress distribution in the current structure?


    Łukasz Skotny Ph.D. - 2019-08-29 07:11:45

    Hey Niels!

    I'm not sure what you mean by UR stress. I think we are talking about the same thing here, to be honest. When you have a less rigid element it takes less load, leading to less stress. This is how it is easiest to notice this, but I would still reference this as a "rigidity" problem if you are comparing stress levels of various elements and wondering if you should strengthen something to redistribute loads more uniformly, etc. But to that degree, apart from checking deformations of the model, and stress levels, there isn't any particulat "rigidity check" you can perform... so I think we are simply talking about the same thing, but calling it differently.

    For me, stress design is when you have low stress in an element so you make it thinner. This is what most people do. Rigidity design would mean, that you actually think "why" there is less stress in this place and wondering how to change the rigidity of the system to utilize all elements in a similar degree. This is a more complex thing, sure. It requires some understanding of how things work etc. But there aren't more "FEA checks" you perform... it's just thinking mostly, and looking at the same outcomes from a different perspective.

    I hope this makes sense?

    Niels - 2019-08-29 13:35:15

    Agreed. The point I guess I am clumsily trying to get across that stress optimizing by reducing member size without considering its stiffness effects will possibly lead to double work later on. If you consider rigidity from the beginning you'll save yourself headaches down the road. While the stress is often the result and what the client is looking for, the source is the rigidity (and loads obviously, but their contribution is rarely overlooked). This is also what I get from your posts on rigidity.

    BTW, UR has been used as the abbreviation for utilization ratio where I've been employed. Sorry for assuming its generality.

    Have a great day!

    Łukasz Skotny Ph.D. - 2019-08-29 18:08:03


    Nicely put Niels - I think that engineering is full of things you can deal with "now" or have a headache "later".

    Ach, Utilization Ratio... I would never guess that! I'm using "Capacity" rather than "Utilization" in all of my documents, so I had no chance ;)

    Nice to have you around Niels!
    Have a wonderful day!

    Ivar - 2019-07-19 10:59:39

    Hi Lukasz
    Nice blog page again :)

    One thing you could remind us all about: structural FEM solves for displacements u,v,w, that is then translated into strain dl/l that then is again translated into stress.

    So stress is the last product of a long calculation and the most "wrong" in case of rounding errors, and since most people work in linear theory sin(alpha)=alpha and cos(alpha)=1 these u,v,w are often quiet rough, hence strain in the shear directions are floppy and final stress too.

    So any given model might have valid displacements u,v,w but still really wrong stress, if these displacements are not correctly resolved =>
    - how to mesh in consequence, and
    - i.e. when to turn on non-linear geometry.

    I say always: I must ensure results with quasi linear first derivatives of the displacements, to trust locally my stress.

    But all this is very model dependent, and that is where the experience of the FEM modeller comes in, not only to produce nice graphs, but also to check by measurements and tests that the values hold in reality :)


    Łukasz Skotny Ph.D. - 2019-07-19 15:25:56

    Hey Ivar!

    I'm glad that you like the post :)

    Experience in FEA is always a factor of course... but as you wrote, it's bad when someone only tries to produce "nice graphs" and nothing more.
    This is a tricky topic BTW because you need to get the experience "somehow" and I think everybody goes through the "pretty pictures" phase of their career. The trick is I think in leaving it, and not staying there till retirement :)

    All the best

    Magdalena - 2019-04-25 19:27:54

    Cześć Łukasz!
    Świetny blog, właśnie czegoś takiego szukałam. Kopalnia wiedzy, a dodatkowo napisana w rewelacyjnym stylu. Sama przyjemność czytania. Dziękuję i pozdarwiam

    Łukasz Skotny Ph.D. - 2019-04-26 12:24:38


    No bardzo mi miło to słyszeć :)


    Prithviraj - 2017-12-11 15:01:07

    hello sir,
    i have one question, is it true that von mises stress is only used for ductile material? As for brittle material many suggests Max.Principal stress?
    Why it is useful to use von mises stress during post processing?

    Łukasz Skotny Ph.D. - 2017-12-11 17:36:43


    Yes - von Misses stress is used in the ductile material. There are other hypotheses like Tresca-Guest that may be a better fit.

    Why von Mises stress is useful... this is a very difficult question to answer shortly. And I don't think I've made a post about it (great question BTW!). I would say that this is because you get entire stress tensor "shortened" to one value - so it is easy to interpret it, and decide how close to yielding are you. Of course, you lose a lot of data in this "shortening" but the "sense" of overall capacity `usage remains (you just don't know if the "stress" comes from shear or tension or compression or whatever). This means that while von Mises is definitely the most popular tool it is definitely not the only one needed.

    All the best

    Praveen - 2017-12-01 02:41:00

    Sir, you given lot of information that I have to study of it but is there a book of yours so that I can study well. There lot of doubt there in my mind that I couldn't be solve myself.
    I doubt is that, I when found that merging and contact are given I found it that results are same. I couldn't understand why the people will give differently. Give the explanation of simple manner

    Łukasz Skotny Ph.D. - 2017-12-01 13:04:47

    Hey Praveen!

    Sadly, I don't have any books yet. I'm working on one, but it will take some time.

    I'm also not very sure about what you ask with contact. Maybe this will help you (?):



    Have a great day!

    Arun Kumar - 2017-11-15 13:30:13

    Greetings to you Sir
    I have a question sir "If I am doing elastic perfectly plastic analysis and my model is converged at applied loading.Does that mean my model is stable under applied loading or I have to check strain limits or I have to check stress limits in addition to that "

    Łukasz Skotny Ph.D. - 2017-11-15 14:11:21

    Hey Arun!

    The fact that analysis converged does not mean that everything is ok. It simply means that the solution was found that met convergence criteria.
    However, it is your job to check if that solution is "acceptable". This means that checking strains and plastic collapse is your responsibility.

    Hope that helps :)


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