Dear Reader,

I hope you have had a good start to the week. I will cover the following in this edition of the CM Videos Newsletter where I share my perspectives on all things computational modelling:

1. Technical Reflections: Periodic Boundary Conditions in Open-Hole Testing
2. Behind the Scenes at CM Videos: An Oasis of Discussion
3. Quote of the Week: Suffer Now, Live a Champion.

Lets get into the newsletter.

Technical Reflections

Periodic Boundary Conditions in Open-Hole Testing

I published the following video on my YouTube channel where I showed how one can use Periodic Boundary Conditions to study open-hole tensile testing of specimens. If you are yet to watch the video, please find it below.

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Open Hole Tensile Test

In structural designs, the open hole strength refers to the tensile strength of a material with a hole or notch, as opposed to the tensile strength of an unblemished, uniform cross-section material. This concept is critical in understanding the behavior of materials under tensile loads, especially in scenarios where perforations are necessary for functional reasons, such as bolt holes in structural steel plates or openings in concrete elements for utility passage.

The presence of a hole introduces stress concentrations around the edges of the hole, which significantly affects the material's ability to carry tensile loads. The stress concentration factor (SCF) is a multiplier that quantifies how much stress is increased at the critical point of stress concentration compared to the average stress across the section. The open hole tensile strength is thus lower than the tensile strength of the intact material due to these localized increases in stress.

The Open Hole Tensile Test is a popular test in structural engineering which is used to obtain the open hole strength of the material. It helps objectively quantify the effect of a stress concentration around the hole or notch during a tensile test. This will inform the actual strength values that a structural engineer will use in design calculations rather than the manufacturer quoted tensile strength of the material. Factors that affect the Open hole tensile strength are: hole size, specimen dimensions, material type/properties, loading conditions, and surface conditions/finishes. In this reflection, we explore in more depth the impact of loading conditions on the Open-Hole Tensile Strength.

Periodic Boundary Condition (PBC) and Open Hole Tensile test

As stated above, loading conditions imposed on the test specimen would have a significant effect on the open hole tensile strength. Traditionally, numerical investigations would be based on a Dirichlet Boundary Condition (DBC) where specific displacements/forces are applied directly on the specimen to impose the desired tensile load.

What if one decides to use a Periodic Boundary Condition argument in imposing a tensile loading history within the test specimen? This was what I did with this video. To do so, I did the following:

1. Geometry: I referred to a paper by Prof Stephen Hallet from University of Bristol, UK about the combinations of hole size, specimen length in defining accpetable geometry for the test specimen. Prof Hallet with his team found that the ratio of width to hole diameter (W/D) should be 5. That means, for this instance where I used a hole of diameter, d = 4 mm, the width was, W = 20 mm. Also, the ratio of length (outside the grips) to diameter (L/d) is 20. That means my test specimen was 80 mm.
2. Periodic Boundary Condition: I therefore used the geometry described above in my study. It is a 2D system with clear edges (horizontal and vertical). I then meshed it uniformly so we obtain symmetric (or periodic) meshes with equal number of nodes on corresponding parallel and opposite edges. To impose PBC, I had to resort to my MATLAB-based PBC-generating plugin called PBCGen2D which you can obtain via this link.
3. Simulation Results: As expected, the deformation for such a centrally positioned load, on a homogeneous material type as tested here, resulted in symmetric deformation with parallel and opposite edges deforming co-operatively. There was no visible wavelike edge effects due to the symmetry and homogeneous material type.

Implication for Design

In engineering design, particularly in aerospace, automotive, and civil engineering, accounting for the reduction in tensile strength due to open holes is crucial for ensuring safety and structural integrity. Designers often use factors of safety and stress analysis (including finite element analysis, FEA) to assess the impact of holes on structural performance and to specify minimum material thicknesses, reinforcement strategies, or alternative materials to compensate for the reduced strength.

Moreover, design guidelines and standards often include empirical formulas or correction factors to estimate the open hole tensile strength based on experimental data and theoretical models. In the context of this video, a yet again widespread use of PBCs in a non-standard way has been shown. We have not only limited PBCs to RVE micromechanical modelling studies, but here it is used in a macroscale specimen analysis. It is possible because of the unique design of the specimen with clear edges that are symmetric and homogeneous.

Behind the Scenes at CM Videos

An Oasis of Discussion

I received a common on one of my CMVideos YouTube Channel this week which read as follows:

The reason why I am highlighting this comment is that this is precisely the values I hold dear in the CMVideos business. I set up a YouTube channel to make videos to help many take up and do well with computational modelling. I have to date published 150 videos designed to do precisely that. I have quite a lot of comments and over 300,000 views.

The aspect that I enjoy the most is the interactions on comments in my videos. I think it is above the normal expectations for channels my size and focus to get so much good comments and reviews on nearly all my videos. This is kudos to the very exciting and engaged audience that I am building on this channel.

So, reading that the channel and especially the comments section is an oasis of discussions speaks to me very much as it is what I set out to do. I want to engage my community by reading and responding to their comments. I set out to offer indepth comments on any questions I receive in the channel so that not only the one who asked will benefit but since answer remains there for ever, future persons will benefit from the same. Therefore, it made my day reading that comment and it tells me I am moving in the right direction and should keep the computational modelling creative fire burning bright.

Quote of the Week

Suffer Now, Live a Champion

I am taking my quote for the week from a quote in Ali Abdaal's book - Feel Good Productivity - in which he was discussing about the hustle culture: pros, cons and pitfalls. I was drawn to this quote, in the book, from Mohammed Ali which goes as follows:

This quote reflects Mohammed Ali's incredible work ethic, determination, and the mindset that helped him achieve greatness in his career and become a global symbol for resilience and courage. There is something in there for us to learn from.

One thing that struck me is how this quote is so true in the life of an academic and a student. To climb the academic ladder, you will often have to work late hours into the night, writing papers that might be rejected a few times before they are accepted. You will write a lot of grant applications, chasing for a few funds that is competitively bidded for by many. More often than not, such applications get rejected but you have to keep soldiering on. As a student, you get to research on differs topics and many days go home with the experiment or model not working out. It seems and endless cycle of little or no progress.

As you go through these ardous journeys, you have options of resting, revising and repeating the process. The option you do not have is to stop or quite. No, this should never be on the table. Like Ali, you may not enjoy every minute of your academic struggles but if you persevere and accept the suffering of today, you are going to come up at the other end successful. Ones success can be achieving the degree classification you enrolled for i.e. PhD, MSc, MEng and others. Carrying the title of 'Dr So-so-and-so' is a feat only a few in the soceity have been able to achieve. Estimates have suggested that in countries with advanced education systems, less than 2% of the population holds a PhD. So, bear that in mind, you are only 2% of the population that holds a PhD and so you are special.

Welcome the hard knocks of training today that you may become a champion, a special breed, the cream of the soceity and the valued personalities of your community. Whatever your goal is, please keep going and never give up. It is this mentality that made Mohammed Ali the greatest boxer of all time. What 'Greatest' title do you want to become? Keep going!

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.

If you know anyone who would benefit from reading these reflections, please do share with them. If there is any topic you want me to explore making a video about, then please do let me know.

I wish you a wonderful week and I will catch up with you in the next newsletter.