Hi Francesca,

As for the continuous enrichment part of X-FEM (i.e. crack-tip) you can 
look into FE_Enriched 
<https://www.dealii.org/developer/doxygen/deal.II/classFE__Enriched.html> class 
and the paper with implementation details. 
Note the key difference in point-of-view: FE_Enriched does cell-based 
enrichment, i.e. all nodes will be enriched the same way 
with given function(s). One can still mix things with FE_Nothing to have 
different enrichment with different parts of the domain to
get conforming FE space. This PR 
<https://github.com/dealii/dealii/pull/6277> from my student will make it 
easier to do. 
For the discontinuous part (Heaviside) FE_Enriched might be ok as well, but 
I guess in this case construction of quadrature rule and integration is the 
major PITA.

Regards,
Denis

On Wednesday, May 23, 2018 at 11:47:52 AM UTC+2, Francesca Fantoni wrote:
>
> Good morning everyone,
> I am currently working on crack tracking algorithms in the context of 
> Linear Elastic Fracture Mechanics for three dimensional problems.
> I was wondering if in deal.ii  there exists any code gallery related to 
> the implementation of quarter-point elements and the computation of SIFs 
> along the Crack front.
> Alternatively if there exists some code related to the use of X-FEM for 
> fracture mechanics.
> I am not able to find any code related to these problems...I found some 
> codes related to the use of the phase field method in fracture mechanics, 
> but we are interested in using a different approach to model the presence 
> of the crack.
> Could anyone kindly guide me?
> Thanks very much
> Francesca
>

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