Coupling of peridynamic theory and the finite element method

The finite element method is widely utilized for the numerical solution of structural problems. However, damage prediction using the finite element method can be very cumbersome because the derivatives of displacements are undefined at the discontinuities. In contrast, the peridynamic theory uses displacements rather than displacement derivatives in its formulation. Hence, peridynamic equations are valid everywhere, including discontinuities. Furthermore, the peridynamic theory does not require an external criterion for crack initiation and propagation since material failure is invoked through the material response. However, the finite element method is numerically more efficient than the peridynamic theory. Hence, this study presents a method to couple the peridynamic theory and finite element analysis to take advantage of both methods. The regions where failure is expected are modeled using peridynamics while remaining regions are modeled utilizing the finite element method. Finally, the present approach is demonstrated through a simple problem and predictions of the present approach are compared against both the peridynamic theory and finite element method. The damage simulation results for the present method are demonstrated by considering a plate with a circular cutout.