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6 W H I T E P A P E R Finally, two other parameters listed in Rocky's interface are required to simulate breakage using the Tavares Breakage Model [7]: The minimum specific energy that can cause damage to a particle, e min , and the minimum particle size. The minimum particle size parameter will determine the minimum size fragments can have after a breakage event and, hence, the size distribution of each breakage event will be guided by this parameter. 3 DISCRETE BREAKAGE The Discrete Breakage model is the first proposed approach to simulate breakage of solid DEM particles. It was described both in two dimensions [8, 9] and three dimensions [10] at the end of 1990s. In this approach, DEM particles are represented by a cluster of elements that can also behave like DEM particles. Most DEM codes use a combination of spheres connected to each other to approximate a particle shape, but when such particle is broken, volume conservation is not guaranteed. Rocky uses tetrahedrons, allowing for representation of any particle shape through this approach, which preserves volume and mass. The bond between each of those elements can withstand tensile stresses up to a specified limit. The standard collisional contacts can be applied between whole particles or particles and boundaries, whereas these collisional contacts cannot withstand tensile forces unless an adhesion process is being simulated. Examples of these contacts in two dimensions are shown in Figure 2. Stress state inside a particle to be broken can be calculated from the forces on the bonds. This approach is similar to a Finite Element Method (FEM); the difference is that in an FEM model, the elements are deformable but connecting joints are not, while in Discrete Breakage, the elements are not deformable but the joints are. Breakage happens when particles are subject to collisional contacts, cracks are propagated, and fragments are created by gradually removing the "glue" on joints that keep the particle together. The elements' detachment is subject to chosen breakage criteria and can be based on surface energy or shear stresses. The criteria implemented in Rocky are presented in this work. Figure 2: "Glued" and "Collisional" contacts example of two dimensional particles subdivided into elementary triangles. Adapted from [8].

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