I joined imechanica almost a year ago and I've been frequently following its interesting discussions, even the most animated ones. I think that a place like this is ideal to foster the exchange of ideas in the scientific community;

Moreover it is fantastic as a simple student like me can interact and easily ask questions to the most important researcher in the field of mechanics.

Hence, I thought it would have been the right place to pose a question which I believe is quite controversial. The debate I would like to open is about the future of meshless methods, are they still valid? It is worth to keep investigation in this area?

High Performance Computing MSc+Ph.D. position available at the University of Glasgow on Massively Parallel Brain Surgery Simulation with the extended finite element method (XFEM and FleXFEM)  (University of Glasgow) -- funding body is EPSRC.

One year MSc in HPC in Edinburgh (all costs covered by funding) + 3 year Ph.D.  and access to HecToR, one of the world's largest super-computer, including training with experts in massively parallel simulation (10,000+ processors).

Supervisor: Dr Stephane Bordas,Dr Lee Margetts (Manchester)

Collaborators: Prof. Ray Ogden and Prof. Gerhard Holzapfel

I am working on crack propagation . I am trying to figure what factors should be taken into account when the crack is being propagated using XFEM.

I am especially interested to know what happens to the additional dof's corresponding to enriched nodes. Once the crack is propagated and crack tip is at new location , we add new dof's corresponding to enrichment functions , but what happens to the information stored by the dof's of previous enriched nodes,do we forget them altotgether , or do we map it to the new enriched nodes?

Hi,

I am using a X-FEM Matlab code found here http://people.civil.gla.ac.uk/~bordas/xfemMatlab.html"]http://people.civil.gla.ac.uk/~bordas/xfemMatlab.html

In branch.m/branch_node.m (both functions of radius r and angle theta) crack tip fields are defined...and questions arise.

% Functions

f(1) = r2 * st2 ;
f(2) = r2 * ct2;
f(3) = r2 * st2 * ct;
f(4) = r2 * ct2 * ct;

-these functions are not the same defined e.g. in (Fleming,1997) or (Sukumar,2000) etc...why?

 their derivatives are then considered:

(here for function f(3))

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.  

Comments and feedback of the following paper would be appreciated.

Abstract:

A new technique for the modelling of multiple dislocations based on introducing interior discontinuities is presented. In contrast to existing methods, the superposition of infinite domain solutions is avoided; interior discontinuities are specified on the dislocation slip surfaces and the resulting boundary value problem is solved by a finite element method. The accuracy of the proposed method is verified and its efficiency for multi-dislocation problems is illustrated. Bounded core energies are incorporated into the method through regularization of the discontinuities at their edges. Though the method is applied to edge dislocations here, its extension to other types of dislocations is straightforward.

Hello,

The aim of this writting is to give a brief introduction to the eXtended Finite Element Method (XFEM) and investigation of its practical applications.

Firstly introduced in 1999 by the work of Black and Belytschko, XFEM is a local partition of unity (PUM) enriched finite element method. By local, it means that only a region near the discontinuties such as cracks, holes, material interfaces are enriched. The most important concept in this method is "enrichment" which means that the displacement approximation is enriched (incorporated) by additional problem-specific functions. For example, for crack modelling, the Heaviside function is used to enrich nodes whose support cut by the crack face whereas the near tip asymptotic functions are used to model the crack tip singularity (nodes whose support containes the tip are enriched).