## 2 Numerical Methods
### Erosion Scheme
In particular, the present code can easily be extended to simulate hybrid drilling methods, such as PDC cutting combined with a high-pressure CO\({}_{2}\) jet [21]. ## 5 Conclusions

A numerical method for predicting the cutting force and the volume of removed material, in rock cutting with a single PDC cutter, was developed and validated in this paper. There follow some concluding remarks:

* The numerical method includes a damage-viscoplasticity model to describe rock fracture in PDC cutting, and an explicit time stepping approach to solve the global equations of motion with frictional contact boundary conditions. The code is implemented in the Matlab (alternatively Octave) language with a mex-file (compiled from Fortran native code) to speed up the loop over element level computations. As such, the code can perform a 12 mm stroke of PDC cutting with a single cutter (9.5 mm diameter), on a mesh with ~500,000 linear finite elements, in 2 days on a typical powerful laptop (time steps being ~3 \(\times\) 10\({}^{-8}\) s). If parallelized, a longer stroke or multiple cutters within the same CPU time are feasible. * An erosion algorithm based on a conservative damage criterion was presented. Accordingly, an element is considered eroded if both the tensile and compressive damage variables exceed a threshold value. However, the elements are not removed from the mesh but retained as ghost elements, with no contribution other than masses in the lumped mass matrix, to preserve the balance of mass. Moreover, a node in the potential or actual contact nodes is removed from the list of contact nodes if all elements connected to it are deleted (i.e., are ghost elements). * The method predicts the cutting force in PDC cutting of granite for a single cutter with a good accuracy at variable cutting depths and rake angles. The cut grooves have realistic features. As such, the method serves as a possible platform to be extended to simulate hybrid PDC cutting, where the mechanical cutting action is facilitated by some nonmechanical agent, e.g., thermal jets or microwaves. This is a topic for future developments of the code. This research received no external funding. ## References

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