Theextendedfiniteelementmethod(X-FEM)hasrecentlyemergedasanalternativetomeshing/remeshingcracksurfacesincomputationalfracturemechanicsthankstotheconceptofdiscontinuousandasymptoticpartitionofunityenrichment(PUM)ofthestandardfiniteelementapproximationspaces.Levelsetmethodshavebeenrecently