This study presents an approach to couple IsoGeometric Analysis (IGA) with PeriDynamics (PD) and eXtended Finite Element Method (XFEM). It removes the need for mapping from the parent space to the parametric space as part of IGA. The PD points in the parametric space are governed by the kinematics of control points in the physical space. Therefore, the total Degrees of Freedom (DoF) remains the same. The Jacobian and the strain components at each PD point in the parametric space are computed by employing the PD differential operator. Cracks are simply introduced by removing the interactions among the PD points. The appropriate enrichment functions are activated based on the crack position within the element in the parametric space. The capability of this approach is demonstrated by computing the displacement and stress fields in a curved plate with and without a pre-existing crack.