Boundary node types and Periodic Boundary Conditions | Is Stress measure from ABAQUS True or Nominal Stress? | Impossible Productivity

Published 11 months ago • 8 min read

Hello Reader,

Good day to you wherever you are reading this email from! I wish you a wonderful weekend ahead.

Here are the contents of this newsletter:

  1. Technical Reflection: Boundary Nodes and PBCs
  2. Question of the Week: Is Output from ABAQUS True or Nominal Stress?
  3. Quote of the Day:

Let dive in!

Technical Reflection

Boundary Nodes and Periodic Boundary Conditions (PBC)

As some of you may know, I am working on a book about Periodic Boundary Conditions. I did some writing this week and loved it. I am going to reflect here based on an excerpt of what I was discussing in the book and this is the concept of boundary nodes.

I will start with a definition of boundary conditions taken from my previous book, which goes as follows:

"In the context of finite element modelling, a boundary condition (BC) is a set of constraints imposed on nodal coordinates located on the boundaries of a virtual domain. It is also the condition that must be satisfied by a solution to a differential equation associated with the physical problem under investigation."
- Taken from Okereke, Keates (2018), Finite Element Applications: A Practical Guide to the FEM Process, Springer.

A key clause in that definition is the reference to: nodal coordinates located in the boundaries of a virtual domain. The set of nodes that are located at the boundaries is what I describe here as boundary nodes. They are absolutely important as they are the nodes upon which boundary conditions are specified. When we talk of boundary conditions, we are focusing on the boundary nodes.

I identify three types of boundary nodes and these, I argued in my forthcoming book to be grouped into the following:

Fully external nodes: This refer to a set of boundary nodes that bound the given virtual domain. They are located on the extremities of the virtual domain and they make it easy to access and apply boundary conditions on them. This is shown in figure (a) above. Most structures (without cavities in them) are modelled as fully external boundary nodes.
Fully internal nodes: This is a set of nodes are are located inside a virtual domain as shown by the red circles in figure (b) in the picture above. For such a system, the boundary nodes are locked inside and will require a special/different type of boundary condition to access them. One common type of boundary condition for such system is the pressure loads. An annular structure (as shown above) represents a good example of a structure that has fully internal nodes.
Partially internal nodes: This type of node is neither fully internal nor fully external. They are mid-way and can be represented as shown by the red circles of figure (c) above. They have some parts of it constrained internally while some seem more exposed to the external boundaries of the domain. A good example of a structure that will have this feature is any material that has a crack (thin crack) in them.

Implication: Distinguishing these three types of boundary nodes is important as it will determine what sort of boundary condition can be imposed on a given type of virtual domain. Most of the specifications of periodic boundary conditions rely on the fully external nodes. Clear boundary nodes that are collinear and directly opposite each other are supposed to be imposed with the PBC constraint equation. Where internal nodes (fully or partially) exists, it is not always straightforward how the PBC for such domains can be imposed. This is why, understanding boundary nodes, is important when we consider applying boundary conditions. This understanding will help you determine whether it is more appropriate to use a Dirichlet style boundary condition over use of a periodic boundary condition.

Question of the Week

Is stress measure from ABAQUS True or Nominal Stress?

This is a question that is always asked by students. I am taking this question of the week, again from a comment on one of my videos on the CM Videos YouTube channel. The question is taken from this video: How to get STRESS-STRAIN curve in ABAQUS using 3 Approaches. In that video, I showed three approaches for extracting the stress-strain plots from an ABAQUS simulation. These are: (a) localized (b) volume-averaged and (c) equivalence-equivalence approaches. The stress-strain plots were compared against the three methods with interesting results. The commenter nicely spotted that there is a difference between the stress measures generated from the three approaches and hence the question about what stress measure from ABAQUS actually represents.

Question

Very nice way of explaining the concept sir. Sir, can we extract directly the stress strain plot from the reference point without first extracting force displacement plot from the history output as explained in 3rd experimental equivalence approach? Also, [are] the first two plots true stress-strain plots and the last one approach (experimental equiavence) is engineering stress strain plot?
- Comment by @AnuragGupta-op7uz on the video: How to get STRESS-STRAIN curve in ABAQUS using 3 Approaches.

Answer

Thanks for the comment. A really good question.
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You certainly cannot extract stress or strain variable from the reference point. This is because the reference point is a nodal point and stress and strain measures are variables extracted from an element set rather than a nodal set. Also, the first two plots generated from localization and volume averaging methods are true stress and strain values. To be precise the stress is a 'Cauchy stress' (an equivalent true stress) measure. It corresponds to the force per unit current area.
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For strain, it is a bit complicated as ABAQUS handles strain measures differently. The one shown here is what ABAQUS describes as an integrated total strain - which represents strain obtained by integrating the strain rate of the simulation numerically. It is a bit complicated but will depend on the type of simulation you are doing and the type of solver (ABAQUS Standard or Explicit). Other more common strain measures are the logarithmic strain (LE) and nominal strain (NE). For most cases, and like the case considered in this video, the total strain E11 (along the x-axis) can be assumed to be representative of a true strain but if you do want to test this out yourself, then do so.
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The values from my last approach (experimental equivalence) is definitely an engineering stress-strain plot as a force measure (though current as we tracked it with time) is divided with an initial area. In the problem considered, the area remained the same throughout the simulation. In which case, the current area was equivalent to the original area (since there was no change) hence the equivalence between this approach stress-strain plot and those of the other 2 approaches.
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What would be ideal is to track the area values as a function of time and the force values as a function of time (this later already exists). To do so for the area, a coding with Python script will be appropriate. Currently, at the first time-step, I used my Python script to extract the area. I need to rather do the extracting across all time-steps or frames of the simulation. If this is done, then the force divided by that current area (per time-step) will yield a true stress-strain plot even with my third approach.
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It is a long explanation but I hope this makes sense to you. Let me know in the comments if there are further questions.

Quote of the week

Impossible Productivity Standards

My Quote for the week is taken from my re-reading of Oliver Burkeman's book - Four thousand weeks - which I read and reflected quite a lot about last year. I believe it is one of my most loved Productivity book. Here is the quote which is posed more as a question than an actual statement:

Are you holding yourself to or judging yourself to standards of productivity that are impossible to meet?
- Oliver Burkemann, author of Four thousand weeks.

In the world of productivity-obsessed millenials, the question from Mr Burkemann should draw our careful consideration. It is undeniable the benefits of productivity and many are committed to it. There are lots of books and tools to help amplify our productivity and it is possible due to the near ubiquitous availability of these resources that many are now setting productivity expectations for themselves that can be deemed impossible.

People are now craming a lot into the hours of the day that can only realistically be achieved if the wonder of cloning of oneself has been achieved. I am guilty of this. You simply need to look at my calendar for the day as well as my daily to-do list to see how impossible the things I put in there.

First, I am a husband and father. I need to spend time with these loved ones. Yet, I have these objectives of publishing the best videos for my YouTube channel at least once a week. I am working on new software products which require me to write codes to help my audience. I am working on book manuscripts where I commit to writing 1000 words everyday. To achieve the later, I have to research into the ideas, understand them and be able to communicate them in a clear, eloquent, logical and understandable manner for the future readers of the book. I also have to write journal papers with a view to write 3 high impact factor journals per year - where I am first author. I have to teach my 4 courses in my university. I have to also supervise my PhD, MSc, MRes, MEng and BEng students. That is on top of also doing my administrative roles within the university. In my personal life, I have to also play the role of a minister within my local church.

I want to achieve all these - or at least - address them every week. I try to put these on the calendar and to-do list. The reality is that it is impossible and this sort of extreme productivity is not good for me and not for you too. This is why the question from Mr Burkemann is rather pertinent, and I finish by posing the same to you: Are you holding yourself or judging yourself to standards of productivity that are impossible to meet?

One caveat for my case is that though the above are my expectations, I am rather not too hung up on them. I put them in my schedule as a road map of where I am going rather than an pre-determined and contractual destination that I MUST arrive at. Therefore, even if I do not achieve them, I am not going to be hard on myself. I just want to keep moving, and if I write 100 words per day in my book instead of 1000, that is progress though only 10%. I am happy with that. I will suggest you do the same in your work, if you find yourself in the same productivity loop as myself.

Thank you for your patience in reading to the end of this newsletter. It was rather longer than I intended but I hope there are bits in it that are of value to you. I will catch up with you next week and in the mean time, have a wonderful weekend and God bless you.

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Thank you for reading this newsletter.

If you have any comment about my reflections this week, please do email me in a reply to this message and I will be so glad to hear from you.

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Lets keep creating effective computational modelling solutions.

Michael

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I am an university academic, author and content creator who specializes in all things computational modelling. Please join over 800+ computational modelling enthusiasts who read my weekly (Friday) newsletters where I reflect on finite element modelling, engineering, AI and personal development journeys. I also offer insights on different aspects of the academic journey that have led to my becoming an Associate Professor.