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.
