A short story about Numerical Bulk Modulus


Dear Reader,

Good day! Hope you are having a fine day today.

Here is another newsletter as we continue to create effective computational modelling solutions to any of your modelling challenges. Today, I wanted to tell a story that informed my two latest YouTube videos. Lets get into the newsletter


Technical Reflections

A short story about Numerical Bulk Modulus

As you know, I make videos on the CMVideos YouTube channel and most of the videos are drawn from my research and teaching. Quite often I get requests from viewers asking me to make one type of video or another.

So, about two weeks ago, I came back from church and after spending time with my family, went into my study to do some work. I decided to quickly check my YouTube analytics to see how the videos are doing. I read a comment from oneManishSingh-gc5fv, a viewer on my channel, placed on my video titled: The SUPER EASY way to model LATTICE Structures. It is an old video but the video is about how to create a virtual domain for this unique type of face-centred cubic lattice structure. Here is the quote from Manish:

Great video! Thanks! Can you make a video on calculating bulk modulus of lattice structure.
- ManishSingh-gc5fv (left of YouTube video titled "The SUPER EASY way to model LATTICE Structures"

I wanted initially to reply saying I was not going to explore this topic as I had never dealt with bulk modulus determination from a numerical experiment. But before I sent my reply to the comment, I decided to look briefly into the whole topic.

I immediately Googled what Bulk modulus was about especially in terms of how to determine it numerically. Clearly, there was not a lot to explain how to determine it experimentally. I then went on to get a definition of it and here is what I define bulk modulus to be:

Bulk modulus is an elastic property of material that measures its resistance to compression when every of its surfaces is under pressure.

So, the key features of any numerical experiment that will investigate bulk modulus is:

  • It has to be an elastic analysis (so only elastic properties will be required)
  • All faces/surfaces of the virtual domain must be constrained by pressure load and deformable
  • Compression would be a better way to determine the bulk modulus.

So, bearing all these in mind, I decided to then sketch out an experiment that will consist of:

  • A homogeneous cubic block of material (polypropylene for example)
  • All 5 out of six surfaces will be constrained in one axis (say x-faces in x-direction) but free to deform in all other directions
  • The only remaining free surface (the sixth surface) will be imposed with a pressure load, Po which will then create a deformation within the structure.
  • In the end, determine the volumetric strain due to the deforming pressure load.
  • I will also find the equivalent pressure load, dP within the virtual domain, which is different from the applied pressure load, Po

One I had this clear picture in my mind, I quickly designed the virtual experiment in ABAQUS, determine the volumetric strain as well as pressure load, and then using the formula for bulk modulus, obtained the numerical bulk modulus. I became curious as to how reliable this was. Then I went on to calculate the bulk modulus for a homogeneous material analytically and then got the same result. That pleased me immensely as now I have something I could share with Manish.

As it was all very easy, I quickly set up my filming studio and filled the video showing my findings and published it a few days later under the video shown below. I went on to also do some work on an actual lattice structure but that will be a story for another newsletter. For now, enjoy the video below.

video preview

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 by clicking on the link below. I wish you a wonderful week and I will catch up with you in the next newsletter.

Lets keep creating effective computational modelling solutions.

Michael


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