## 2 Materials and Methods
### Discrete Element Method
In particulate systems, the interactions between particles and boundaries induce shear forces, denoted by the tangential component of contact. Previous research [30; 31] has explored the relationship between the energy resulting from shear-normal impacts and the wear rate in mechanical contacts. These studies emphasize the significant impact of shear component-related energy on surface material removal rates. The analysis of wear within this model delves into the concept of shear intensity, a fundamental measure representing the power transferred per unit area. The application of shear intensity in this model provided a method for qualitatively assessing wear phenomena. By quantifying the power transferred per unit area during collisions, the model can offer insights into the extent of wear on geometric surfaces. This energy metric finds application in abrasive wear models, particularly in assessing shear wear on geometric surfaces. The model can be directly correlated with wear phenomena, facilitating the determination of abrasive wear on geometric surfaces. All forms of intensity derived from boundary collision statistics are calculated per individual boundary triangle [32]. \[I_{b,T}^{Shear}=\frac{\sum_{\kappa=1}^{N_{\kappa}T}\left(W_{\kappa}^{Shear} \right)_{b}}{A_{T}\Delta t_{out}} \tag{4}\]  
where \(A_{T}\) is the boundary area, \(\Delta t_{out}\) data collection time interval and \(W_{\kappa}^{Shear}\) is the shear work of a particle-boundary collision. For additional information, please refer to [32]. Additionally, an extra wear model, namely the Archard model, was incorporated. This model, based on the research of [PERSON], ref. [33] suggests that the amount of material removed from the surface correlates directly with the frictional work executed by particles in motion on the surface. Despite qualitative analysis, we have the ability to visually depict surface wear more elegantly and streamline the summation of surface wear, exclusively within the final idealized model. Refer to literature sources [32] for a detailed discussion on the exact computations of coefficients. Due to conciseness, a comprehensive explanation is omitted here. The coupling between DEM and FEA enables the prediction of stress and strain responses in structures under bulk material loading conditions. An essential objective involves determining the node forces according to the applied load for every element. [PERSON] et al. [34] showed while this process is straightforward for basic meshes, it necessitates further consideration when accommodating modern high-order shell and volume elements. In this study, coupling DEM-FEA was conducted through a well-established workflow within the Ansys Workbench environment, specifically between Ansys Rocky and Ansys Transient. By running Boundary Collision Statistics, we can capture the average collision forces exerted on boundaries. These forces can be exported to external software for structural analysis. Typically, boundary conditions for such analyses require nodal forces, which are the forces acting on the vertices of the triangles forming the boundaries. Thus, to streamline the data transfer to finite element software, Rocky offers these nodal force values, derived from the collected forces per boundary triangle. The determination of these forces is achieved using the following expression [32]. \[F_{b,T}^{Y}=\frac{\sum_{\kappa=1}^{N_{\kappa}T}Y_{\kappa}^{Y}}{\Delta t_{out}} \tag{5}\]The impulse associated with the total force exerted over a boundary triangle during a collision is denoted as \(I_{X}^{\gamma}\) where \(\gamma\) is a component for any of the Cartesian components. the summation in this equation encompasses all collisions recorded against boundary triangle T during the data collection interval \(\Delta t_{out}\). To derive the nodal force values, it is assumed that collisions over a boundary triangle are uniformly distributed, allowing the resulting force on the boundary triangle to be evenly divided among its three vertices.