The magic of Extended Finite Element Modelling (XFEM)
Dear Reader,
Greetings! I am so excited to welcome you to this week's edition of my newsletter. As usual, the vision is always to share topical issues around computational modelling; behind the scenes at CM contents, and other inspiring reflections. So here are the features I am writing about this week.
- Pray for Turkey and Syria
- Technical Reflections: The magic of XFEM: The case for self-healing composites
- Behind the Scenes at CM Videos: ChatGPT and optimized YouTube titles
- Quote of the Week: The AI Revolution and History
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Pray for Turkey and SyriaI am saddened by the terrible news of the earthquake that affected parts of Syria and Turkey. It is sad to imagine what the people living there are actually experiencing with so many thousands of death. In such moments, the best of humanity comes to the fore, so if you know how you can support, even with a donation, that will go a long way. Or simply just pray for Turkey and Syria. Photo by Ercin Erturk/Anadolu Agency via Getty Images |
Technical Reflections
The magic of XFEM: The case for self-healing concrete
I have been working over the last two months on fracture modelling of self-healing concrete. This was necessitated by my Erasmus Exchange student - John Hanna - who I introduced to you a few weeks ago. John has been using the XFEM method to track the fracture of microcapsules (red regions) within a concrete material (gray region). The use of XFEM is quite magical.
Extended Finite Element Modelling (XFEM) is a numerical implementation of the FEM method specifically targetting the modelling of discontinuities e.g. cracks in materials and their evolution. This is important as traditional FEM methods assumes continuity of the domain. The shape functions that are used to derive the constitutive behaviour of elements demands that there exists continuity between boundaries. Therefore, in specifying the element properties, not only the nodal coordinates need to be specified, one must also specify the connectivities between one element and another.
Element connectivities: To illustrate this, let us consider two elements - 1 & 2 below. They have nodes 1 to 6 but the connectivities between elements 1 and 2 are 6 and 3. This is a requirement for FEM. This connectivity should not be broken.
Preserving continuum in classic fracture mechanics FEM: However, if a standard fracture mechanics analysis is to be undertaken, the requirement of element connectivities has to still be enforced. For example, as shown below, when a crack (shown in white below) splits the connectivities of elements 1 and 2 via their connectivities 6 and 3, the continuum assumption of classic FEM demands that new nodes have to be introduced to preserve the element continuity argument. Therefore a different formulation will be implemented to stabilize the evolution of the crack through the boundaries. There is no possibility of the element itself being split in two.
When elements splits, call in XFEM: However, the magic of XFEM method allows for the element to actually be split into two without having to re-order the nodes or create new nodes. The split is introduced into the element formulation as a discontinuity and a discontinuity functions mathematics is used to allow the element to split without compromising the continuum of the overall model. This is a very excellent feature and models tracts 'truthfully'. The probability of cracks evolving 'naturally' through any part of the element is the greatest attraction to the XFEM method. Though the simulation may apear that the element is actually split but that is not necessarily the case. Rather an enrichment function is applied on the nodal displacements to simulate artificially the separation of the cracked faces. Practically, the elements along the cracked faces/surfaces are enriched with a discontinuous function while element at the tip of the crack has similar enrichment function based on a near-tip asymptotic displacement function.
It was this sort of XFEM that John has been using in his study of fractures of microcapsules within a self-healing concrete. The interesting feature here is that randomly distributed microcapsules are introduced into the concrete mixture using the Monte Carlo Methods that I publish regularly about on the YouTube Channel. We hope to use periodic boundary conditions to simulate the loading of such structures however for now a Dirichlet type boundary conditions is used for this. Looking at the picture above, you can truly see the magic of XFEM and cracks in the concrete seem realistic. However, only experiments can truly show if our results are representative and we are working on this for now.
Behind the Scenes at CM Videos
ChatGPT and Optimized YouTube TitlesOne use of ChatGPT that I am finding really useful is how it can be ued to help optimize the titles I give my videos. In the past, I had to think about variants of titles to my videos that can make them more likely to be clicked by users. This is something I believe will continue to be in vogue that is using AI assistants like ChatGPT to help us with routine tasks as copy editting, titles videos and others. How do you think you can use AI with your computational modelling. |
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Quote of the Week
The AI Revolution and History
I stumbled on this fantastic blog by Tim Urban. If you do not know who he is, then he is the famous TED talker who explored what is going on inside the mind of a procrastinator. Google him and get to know his work.
He is rather also known for an article on his WaitButWhy blog site titled: The AI Revolution: The Road to Superintelligence. I was reading the article this week and have taken my quote for the week from there.
The essence of the quote is that in terms of our expectations of what happens to us, we often have a linear perspective to it. For example, I am X years now, next year, I will be X+1 years and after 4 years, I will be X+4 years. Also, I earn £Q today, if I work really hard, maybe by the promotion, I could be earning £1.2Q which is a 20% addition to my original salary. All these relate to a linear sequence of growth.
In similar reasoning, the understanding we have is often deemed to increase as such slow linear-tracked dimension. However, when AI comes into the field of play, this linear sequence of progression is blown out of the water. This is why the AI revolution is a reality and we are on the verge of something dramatic.
The implication of this for you and me is that we need to start thinking about geometric progression with our outputs and productivities. The evolution of AI and what it can help us do, is simply astonishing and when embraced and harnessed effectively, we will produce geometric-progression outputs.
In your research and work, what do you think a geometric progression of outputs be? It might be publishing 20 papers in one year; teaching students on site, online and via other media in a simultaneous dynamic and truly embodied dimensions. It can also mean producing high quality videos everyday with tremendous engagement. It can also mean far-fetched objectives which at conceptualization stage seem unachievable but with the assistance of AI, we might just about do it.
Thank you for reading a slightly longer newsletter for this week. I wish you a wonderful weekend and also highly productive next week.
Please share with others and let me know in a reply email or comment of YouTube channel what you think about the issues I shared here.
Take care and catch you next week.
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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. 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 Connect with me on: Twitter | LinkedIn | Instagram | Tiktok | Mailing List Other Links
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