Coupling of peridynamics with finite elements without an overlap zone

This study presents a variational approach to couple PeriDynamic (PD) and Finite Element (FE) analyses to take advantage of their salient features. The region of PD can be completely or partially surrounded by a region of traditional finite elements. There exists no overlap (transition) region along the interface of these regions unlike the previous coupling techniques. Therefore, this approach does not require a morphing or a blending function that facilitates coupling over a transition zone. The PD region with an arbitrary geometry is interfaced with traditional local (conventional) elements while satisfying the displacement continuity through Lagrange multipliers. The resulting global system of equations includes the contributions arising from the PD points and the FE nodes. These equations are solved simultaneously without requiring an iterative procedure. Therefore, it is a direct coupling approach. This coupling approach is demonstrated by considering an isotropic plate under tensile loading. Part of the plate is modeled with PD points, and the remaining region with linear triangular elements. The PD region can share a boundary with FEM region or completed embedded in the FE region. The results from the coupled PD/FE approach agree well with those of PD and FE analyses.