Coupled peridynamics and XFEM

This study presents an approach to employ peridynamics in the activation of enrichment functions of the eXtended Finite Element Method (XFEM). It is based on the principle of virtual work while employing the nonlocal stress and strain components. The kinematics of PD points are controlled by the nodal unknowns of the finite elements. The derivatives of the displacement components at each material point are computed by employing the peridynamic differential operator. It is always free of singular strain field regardless of the presence of discontinuity or singularity. By monitoring the stretch between the peridynamic material points, the interactions can be removed to nucleate and guide the crack. The appropriate enrichment functions are activated based on the crack propagation path prior to the next incremental load step. The total number of nodal unknowns remains the same, and the PD calculations do not require the solution of any additional equations.