XFEM bi-material enrichment function

Hi,

I am PhD student and I am working in the field of using XFEM & LSM approach for shape optimization problems. I am at the beginig of my work and I have the following question: for a bi-material type problemhi is well-known that the most simply enrichment function is the abs(phi). My question: is possible to use other continuos function as enrichment function (of course with discontinuos first derivative). For instance  I use the following enrichment function: psi(phi)= 1 (if phi)>0 and psi(phi)=1-2phi (if phi<=0). So, I try to use function with different values of the slops in the 2 different materials ? It is correct or not?

Thanks a lot for any information !!

 gelu 

enritchment function