## 1 Introduction  
Drilling a well into a deep reservoir in a hard formation is technologically challenging and incurs major costs in hydrocarbon operations and harvesting geothermal energy. The major problem therein is the tool wear, which results in long idle times, due to the bit replacement. For this reason, the drill bit (see Figure 1) cutters are made of extremely hard materials. Presently, the leading drilling technology in hard formations (e.g., granite) uses the so-called polycrystalline diamond compact (PDC) cutters, made of synthetic polycrystalline diamonds bonded to a tungsten carbide blade. The drilling action by cutting is achieved by applying a certain weight on the bit (WOB) and then rotating the bit with a torque, \(T\). Design of such drill bits for the extreme conditions, involving high pressure, faced in deep well drilling, requires good understanding of the tool-rock interaction dynamics. Considerable research efforts, both experimental and/or analytical investigations [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15] and numerical studies [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27], have been devoted to rotary drilling with PDC bits. The major aim is either to measure, in experiments, or to predict, in modelling, the cutting force (\(F_{c}\) in Figure 1) as a function of various drilling technical parameters, such as cutting depth (controlled by adjusting the WOB or \(F_{p}\) for a single cutter, in Figure 1), rake angle, cutter size, and cutting speed. Instead of considering the whole rotary bit, the focus of research is often simplified on the tool-rock interaction of a single PDC cutter, described in Figure 1. Moreover, the circular trajectory of the cutters, due to a rotating bit, is usually replaced by a linear path. A numerical model, implemented in a computer code capable of predicting the cutting force, the initiation of fracture, and the progression of fragmentation leading to rock material removal, is of utmost importance in the research and development of PDC cutters and rotary bits. There are basically two numerical approaches in the literature related to rock cutting, the discrete element method (DEM), or particle methods more generally, and the finite element method (FEM). The DEM was applied, e.g., in [16; 17; 18; 21; 22; 25], while ref. [27] gives a review on numerical methods for chip formation in metal cutting. Being based on discontinuum assumption, this method naturally allows fragmentation and crushing to take place in the simulations of rock cutting, as the rock medium to be modelled is discretized into deformable or rigid particles with interaction laws between them. The major drawback is the computational labor, especially in 3D models, required to track the configurations of the particles (neighbors of a particle are not fixed) and possible contacts between them. The FEM, in contrast, is a continuum method, where the discretization results in elements with fixed neighbors. Therefore, modelling large deformations and fragmentation requires special techniques, such as remeshing, element erosion, and contact modelling. However, the FEM is a mature numerical method, that has been successfully used to simulate rock cutting problems, as exemplified in [19; 20; 23; 24; 26]. Therefore, as the computational effort needed is less intensive, and the calibration of the model parameters is less involved, the FEM is chosen for the present study. The above mentioned numerical studies use commercial multipurpose FEA software packages (Abaqus, Ansys, etc.) for rock cutting simulation. The present study aims to develop a 3D numerical platform, tailored to simulate rock cutting with PDC cutters. At this preliminary stage, only the single cutter case is considered. The target is to reliably predict the cutting force and the volume of removed rock in a reasonable CPU time, say over a night or two, for a cutter with a variable size, rake angle, and cutting depth.