When is strong and when is weak by using extended finite element method?

As we know, the extended finite element method has been well used to simulate the localization band propagation and crack propagation without remeshing. It can deal with both strong discontinuity problems (displacement discontinuity) and weak discontinuity problems (strain or acceleration discontinuity). Now, I have always a question: when is strong and when is weak discontinuity using XFEM? In other words, what is the difference for the interpolation function and level set function or other function between strong and weak discontinuity? Thanks.

Liu pengfei