The Extended Finite Element Method (XFEM), has become a well-known tool to
simulate crack propagation problems using non-structured meshes avoiding the remeshing process
usually needed in this type of problems and allowing the inclusion of appropriate shape functions
that reflect the asymptotic displacement field, near the crack tip, via a partition of unity fracture
approach. However, in this kind of numerical applications, all the variables involved have been
considered as deterministic (defined by a single given value), despite the well-known uncertainty
associated to many of them (external loads, geometry and material properties, among others). The
combination of the XFEM and probabilistic techniques is here proposed and formulated allowing
treating fracture mechanics problems from a probabilistic point of view. We present the
implementation of this probabilistic extended finite element method and apply it to the prediction of
the appearance and propagation of a femur’s neck fracture under probabilistic loads.
Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation