## 1 Introduction  
When two or more solids move relative to each other in contact, wear damage occurs in which a part of the material surface is separated by the contact load. The severity and magnitude of wear is determined by parameters such as the material properties of the two objects in contact, relative motion, and surface finish. Plastic shear deformation occurs at the initial defect position when the contacting objects are experiencing a sliding motion and the shear load on the contact surface exceeds the critical load. As the shear load is repeated, the accumulated plastic shear deformation is propagated to the surface cracks, and eventually, part of the surface is peeled off. In the design of mechanical equipment, the determination of the optimal friction speed and shape to minimize wear damage is still a major concern [1]. Since wear is a phenomenon in which a part of the material is separated from the raw material due to friction, it is important to accurately simulate the friction load between materials and the material separation characteristics to evaluate the amount of wear. Wear is affected by not only material properties but also the sliding speed, normal force, and friction coefficient. [PERSON] et al. [2], [PERSON] et al. [3], and [PERSON] et al. [4] summarized the relationship between the speed and friction coefficient as factors affecting friction to evaluate the wear of offshore structures due to ice impact but presented only the experimental results due to the limitations of theoretical analysis. [PERSON] et al. [5] calculated the load due to an ice-structure collision by applying finite element analysis but did not extend it to the wear phenomenon. Nonlinear finite element analysis, including fracture material properties and contact elements, was also attempted to simulate wear between metal materials. [PERSON] and [PERSON] [6] defined the load applied to a train rail as the Hertz elastic contact, evaluated the pressure and the contact shape change with formulas, and then calculated the wear amount using the wear equation of [PERSON] [7; 8]. [PERSON] and [PERSON] [9] also performed a finite element analysis in which wear due to the rotation of spherical pins was replaced with 2D planar and contact elements and then predicted sequentially by separating the reaction force and wear amount. Moreover, [PERSON] [10] analyzed the wear of thin plates due to rotational force using 2D planar elements. [PERSON] and [PERSON] [11] also analyzed the wear of a stainless spherical rotating body using 3D elements and contact elements of ABAQUS. However, wear simulation with 3D finite elements has the disadvantages of analysis sensitivity according to element size at the contact surface and excessive analysis time due to nonlinearity of the contact element, so its use is limited to wear caused by metal-to-metal friction and contact. Therefore, the finite element method is difficult to utilize for wear between multiple particles and solids ([PERSON] et al. [12]; [PERSON] et al. [13]). Meanwhile, friction wear between soil and tools is a major design factor in drilling equipment, agricultural machinery, and construction machinery. Coupling analysis of CFD and the boundary element method (BEM) has been applied to the wear analysis of soil and tools ([PERSON] et al. [14]; [PERSON] et al. [15]; [PERSON] et al. [16]). However, since the CFD analysis includes a visco-plastic fluid field, there are problems in efficiency and accuracy. Moreover, since the evaluation object is modeled with the continuum method, the ability to track the behavior of individual particles is limited. However, it is not an appropriate method when wear occurs due to the interaction between particles and structures, such as soil and tools. The discrete element method (DEM) is a particle-based discrete method to calculate the behavior of particles experiencing collision and frictional interaction and is an effective numerical analysis method for tracking the behavior of individual particles.