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eXtended Finite Element Method: Short Course Notes

I taught a short course some time ago on the eXtended Finite Element Method, and thought many people would find the notes useful.  

So I've posted them here, in .mov format (as exported with the Apple software keynote).  The advantage of this format is that, when you click on one of the .mov files, it should open a separate browser.  Clicking in the window will advance the slide. This way you see all the movies, etc, as well as the sequence as it appears when I gave the talk.  There is a way to add audio to this format as well - something I may pursue in the future.  

As always, comments or questions are welcome.  



It is such a nice coincidence for me. I heard so many nice things about XFEM and their application to fracture mechanics problems. Finally, I decided to give it a thorough reading and I started with early paper from Belytschko and Black. Your short course notes will be great help as I can most of the information at one place. One thing I am really missing is audio in the slides, I hope you get a chance soon to work on it.

I really appreciate your help.Thanks


Teng Li's picture


Thank you for posting your short course notes on XFEM. Althrough I haven't had direct experience with XFEM in my research, I'll be happy to learn more about it when it comes. Your course notes serve well in educating potential users.

The format you present the notes online reminds me an earlier post on NanoHUB, a cyber environment including online courses and tutorials, proceedings of seminars, collaborative tools, and an interface for online simulation.  The online presentations available at NanoHUB usually include a video file (mp4 format) with slides and audio, an audio podcast (mp3 format), and a PDF file of the slides.  You can search the full text in the video, then hop between slides to watch content of interest.  In such a way the online presentations are well delivered through NanoHUB. Maybe at some point we at iMechanica should also look into this. 


Henry Tan's picture

Is XFEM a nice choice to simulate dynamic fragmentation processes, which involve a lot of material separations, and contact between fragments?

There has been some work done to model fragmentation (and the ensuing contact) with XFEM-based ideas, but the results haven't been validated against experiments.  So in my opinion it certainly can be done, but how "nice" it is compared to alternatives?  This remains to be seen. 

One should expect XFEM to be less sensitive to mesh structure than cohesive-network approaches.  And in fact Ted Belytschko has shown this for single-crack propagation and branching.  However, it is not as easy to implement. 


Hi John,

What do you mean the 'alternatives' in your post? I have also interests on this issue as described by Tan. Do you know other mehtod to solve such problem?



Hi John,

 Could XFEM couple with fluid flow simulation? Thanks.


Of course. X-FEM is essentially approximation technology.  You can look at it as the use of special elements if you like.  Since one can address fluid flow problems with standard finite element methods, so too can one use the X-FEM.  The key thing would be to identify suitable enrichment functions for the problem of interest. 

Dear John E. Dolbow

Sir I am larning XFEM, and want to simulate thin plate crack problem by XFEM method.

Can you send  me  matlab codes about thin plate of XFEM method. It will help me a lot.

I hope my request will get your favorable response.

 email ID:-

Dear John E. Dolbow

Sir I am larning XFEM, and want to simulate crack problem by XFEM method.

So, please send me  matlab codes of XFEM method. It will help me a lot.

I hope my request will get your favorable response.

 email ID:-

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