Hello,

Very often analysis with X-FEM leads to poorly conditioned system of equations. In attached an alternative approach which controls quality of FE tetrahedral elemens is shown. Approach utilizing Arbitrary Lagrangian Eulerian approach with material forces is shown.

As an example 3D problem involving large strain and displacements is presented,

http://youtu.be/03tQhVDHbQs

Enjoy,

Lukasz 

Pleas have look 
http://arxiv.org/abs/1110.5321
 
This paper presents theory for the Lagrange co-rotational (CR) formulation of finite elements in the geometrically nonlinear analysis of 3D structures. In this paper strains are assumed to be small while the magnitude of rotations from the reference configuration is not restricted. A new best fit rotator and consistent spin filter are derived. 

Regards,
Lukasz