## 4 Conclusions  
In this study, a peridynamic fatigue damage model was implemented in a commercial FEM software. To the best of the author's knowledge, this is the first such usage of integration of a peridynamic high cycle fatigue model within a finite element software. The solving of high cycle fatigue problems is added to the library of problems where peridynamics has been implemented in FEM to obtain a solution, including ductile fracture of metals, fracture of laminated composites, and highly dynamic failures such as impact damage [7]. By utilizing ABAQUS as the underlying structure as in the current and aforementioned studies, more rapid diffusion of the Peridynamic theory is possible in an industrial setting. Current limitations imposed by the Peridynamic theory include limited availability of solutions and limited access to the workings of the theory. Commercial solution methods for the traditional finite element theory include ABAQUS, ANSYS, NASTRAN and others. No such group of packages exists in the Peridynamic theory and most solutions to date have been obtained via (1) customized user coding in FORTRAN or Matlab, (2) the open-source technologies Peridigm and its predecessor EMU, or (3) the PDIFEA methods used here. Limitations imposed by the first two of these strategies include initial time investment to code a custom solution and software limitations imposed by restricted operating systems for the open-source solutions, respectively. By utilizing PDIFEA, there is much less coding required compared to a custom solution and the solution is obtained without investment in new software or computing platforms. One caveat of using a PDIFEA solution is limitations on the theory imposed by adapting the theory to an FEM solver. In the present case, the choice of micromodulus function was predicated on ease of implementation, although other micromodulus functions provide faster convergence rates. While restrictions are placed on PDIFEA, many of the roadblocks imposed by the theory can be offset by benefits. Each Peridynamic collocation point can have tens or hundreds of interactions as opposed to local theories, such as FEM, where  
Figure 13: Crack Length as a Function of Fatigue Cycles. interactions are less than a dozen. Many complex problems that cannot be solved by peridynamic theory in a time-efficient manner can be undertaken with PDIFEA. Various computing methodologies have been proposed in the literature wherein select regions of a model are modeled with Peridynamic theory and the remainder use FEM for a more computationally economical solution. The use of PDIFEA allows for a single solution. Furthermore, PDIFEA allows many of the efficiencies from FEM such as contact algorithms, submodeling, etc., to be incorporated. From the present study, PDIFEA solutions provide an economical solution with similar accuracy when considering implementation in a dedicated Peridynamic code. The rate of crack advance in the present study agreed well with the empirical results over the entirety of the simulation. Crack path trajectory correlated well with empirical results only beginning to underpredict the trajectory beyond 200,000 cycles. For comparison purposes, the custom code solution by [PERSON] indicated successful correlation up to approximately 260,000 cycles [18]. This tradeoff in accuracy at extended cycles may be tolerated in certain industrial applications given the lower threshold for investment in the PDIFEA solution. Conceptualization, K.M., T.X., J.-T.G. and J.T. ; methodology, K.M., T.X., J.-T.G. and J.T. ; software, K.M. ; validation, K.M. ; formal analysis, K.M. ; investigation, K.M. ; resources, J.-T.G. ; data curation, K.M. and J.-T.G. ; writing--original draft preparation, K.M. and L.C. ; writing--review and editing, K.M., L.C., T.X., J.-T.G. and J.T. ; project administration, J.-T.G. All authors have read and agreed to the published version of the manuscript. This research received no funding support. Not applicable.