Dear Reader,

Good day to you, wherever you are reading this from.

I hope you are having a relaxing end to the week and the new month has started with a bang for you. If you are subscribed to this newsletter for a while, you would have noticed that I have not written to you for about a month now. I apologize for that.

This period is unusually busy for me at my day job as a university lecturer. I have been spending a lot of my time lecturing, supervising students, setting assessment items and most recently preparing them for examination. Over the next week, I will be marking a lot of student scripts, so I hope you do understand.

I have tried to prioritize publishing videos consistently on the channel but things will get better when we go over this highly demanding period of the academic year.

This week, I will be reflecting on the following: Unusual Cylindrical RVEs: Do they matter? Let us get into the newsletter.

Technical Reflections

Unusual Cylindrical RVEs: Do they matter?

Back story

Traditionally, multiscale studies involving analysis at a microscale have depended excessively on cubic Representative Volume Elements (RVEs) with clearly determined lengths, widths and heights. Often, these dimensions are the same (hence cubic). It seemed modellers have this unique tool that digs deep into the heart and soul of the structure to magically isolate a cubic RVE. I have not seen a lot of researchers question to validity of this normalized choice. I have not heard questions around what if I decide to use an amorphous shaped RVE, would it still be valid?

In other instances, people have used cubioidal RVEs as shown above. This is merely in cases where directional dependence (in one of the axis - typically longitudinal directions) must be a feature of the study. Consider for example,undertaking a buckling analysis, there has to be a high aspect ratio to the directions which encourages the modeller to choose a length that is often quite higher than the width. In this instance, a cuboidal RVE is necessary.

Beyond these boundary-condition-necessitated constraint for RVE shape choice, is there anything else that compels modellers to depend largely on cubic RVEs? If you decide to isolate an unusual cylindrical RVEs (whether of high or low aspect ratios), does it really matter? Have you wondered about this before?

I once saw a publication where this author was investigating spherical RVEs and there were interesting results from that study? In fact, the author concluded that optimal properties are best determined when a spherical RVE is chosen for most multiscale studies. Unfortunately, I cannot remember the authors again and would have to dig deep in my Mendeley library to find the paper (let me know in a reply if you are interested in the paper).

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Questions worth considering

All these were running through my mind when I began thinking about creating a cylindrical RVE for a particulate composite. The questions I sought answer for when creating the cylindrical RVEs are the following:

1. How can I distribute randomly the particulates within the cylindrical shaped domain of the RVE?
2. Since it is going to be cylindrical, how can I control the efficient distribution of particulates on edges of the RVEs?
3. What appropriate loading schemes will be useful for this sort of study?
4. Could there be an aspect ratio effect in terms of the generated effective properties?
5. Does it matter if I decide to investigate the properties with cuboidal, cubic or cylindrical RVEs?

I am still running the experiments but what I have been able to do this week is offering viewers of the CMVideos YouTube channel, my three-step approach for easily extracting cylindrical RVEs for a particulate composite. If you have not already seen it, here is the video:

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My 3-step process of creating cylindrical RVEs

It was quite easy process creating this sort of RVEs and here are the steps:

• Step 1: Generate randomly distributed particulates within a defined cuboidal RVE. I could do this manually and if you are interested, then check out this video here. However, since I have access to a MATLAB-based software that I developed called GenParticles3Dv1 (to be launched soon, and click here to join the wait list), I therefore decided to use it. It mearnt that I could decide on length, width and heights of the cuboidal RVE. These dimensions should exceed the dimensions of the desired cylindrical RVE. This because of step 3.
• Step 2: Translate the GenParticles3Dv1-generated RVE into an ABAQUS-type RVE. This could happen only by use of a python script, which takes geometric outputs (dimensions, spherical positions and sizes) from GenParticles3Dv1 and bring them into ABAQUS. The python script was automatically generated inside GenParticles3Dv1 which made this second step easy to complete.
• Step 3: Trim the cuboidal ABAQUS-generated RVE to the required cylindrical shape. This mearnt trimming height-wise (to reveal at both top and bottom faces) particulates. Also, an extrude-cut operation within ABAQUS was used to par-down the cuboidal RVE into a cylindrical RVE.

All these were shown and discussed in detail in the video above and let me know what you think about them.

Final thoughts: The jury is still out on the impact of unusual RVE shapes on effective properties. Over the next weeks, I will continue this experiment and hopefully publish to the CMVideos audience on what I am finding with this sort of investigation. In particular, I want to continue seeking answers to the questions I posed above on this topic. Hopefully we will be able to definitively answer the question: does unusual cylindrical RVEs matter in micromechanical modelling studies.