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:

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:

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.

​