## 3 Numerical Simulation
### Results
#### 3.3.2 Breakage Behavior  
In the numerical test, the breakage phenomenon of the specimen was consistent with the experimental result. First, local breakage was produced, and a small platform was formed at the contact point. Then, the stage for crack nucleation and crack propagation followed. Finally, the contact force exceeded its strength, and the specimen broke into two pieces.  
By means of numerical simulation, we could observe the law of morphological changes inside the specimen as well as the specific form of failure. The top view of the overall breakage shows the destruction form and the cracks in the surface layer of the specimen (see Figure 14a). The elementary particles and failed bonds are shown in the figure. The tensile and shear failure of bonds are indicated by arrows and texts (see Figure 14b and Figure 16c).  
The result indicates that most of the broken contacts failed in tension, which was consistent with the theoretical expectations [46]. It is noteworthy that there was a circular area under the loading plane with a significantly smaller number of cracks, which was similar to the result of the experiment (see Figure 6a). Figure 14b and Figure 16c show enlarged images of the cone core after the overall breakage to study the micromechanical process and mechanism underlying the cone core formation. The small images shown in Figure 14 and Figure 16 are zoomed sections of Figure 14a. The transparency of elementary particles was set to 60%, and only particles and cracks in a limited area in front of the cross-section can be observed.  
It is clear in Figure 14b and Figure 16c that most of the bonded contacts in the area under the loading plane did not break after the overall breakage. The image acquired from the cross-section perpendicular to the fracture plane also indicates that the shape of the unbroken area was similar to a cone. Another important feature is that shear failures of bonds could be found at the edge of the cone core. This indicates that there was a relative movement trend between the cone core and the rest of the specimen. Figure 15 shows the velocity of the elementary particles in Figure 14c. The arrow is located in the center of the particle pointing to the direction of the velocity, and the length of the arrow is linearly related to the velocity of the particle. It is clear that particles in the blue region basically moved downward as a whole.  
Figure 14: Morphologies after breakage: (**a**) overall breakage (top view); (**b**) partial enlargement (A-A); and (**c**) partial enlargement (B-B).  
The bond states at different loading stages are shown in Figure 16. The elementary particles and tensile failures on the cross-section B-B in Figure 14a are displayed. All shear failures are shown. The results show that local breakages first occurred at the surface and inside the specimen under the loading plate; most of the cracks exhibited tensile failure, while some cracks in the annular area centered around the loading point exhibited shear failure (see Figure 16a). Since the load continued to increase, shear cracks developed to the inner of the specimen and eventually formed a cone core (see Figure 16b and 18c). The cone core moved downward under the loading plate and ultimately split the specimen into pieces.