## 4 Numerical Simulation
### Influence of Ice Thickness
#### 4.1.2 Influence of Ice Thickness on the Load Characteristics of the Vehicle  
The variation of the stress at the head of the vehicle at different ice thicknesses is presented in Figure 26. Evidently, the stress at the head of the vehicle constantly fluctuates with time. When ice is 10-50 mm thick, the maximum stress at the head is 9.48 \(\times\) 10\({}^{7}\) Pa, 1.09 \(\times\) 10\({}^{8}\) Pa, 1.14 \(\times\) 10\({}^{8}\) Pa, 1.46 \(\times\) 10\({}^{8}\) Pa, and 1.56 \(\times\) 10\({}^{8}\) Pa, respectively. The maximum stress on the vehicle goes up with the increasing ice thickness. After reaching the maximum stress, the stress drops quickly. Figure 27 shows the damage process of ice at different thicknesses when the vehicle breaks ice. Water and air are hidden to indicate the variation of the cloud diagrams clearly. Evidently, the amount of broken ice increases with the ice thickness. When the ice is 10 mm thick, a low amount of broken ice is generated when the vehicle breaks ice. However, a large amount of broken ice appears when the ice thickness increases to 50 mm. In the ice  
Figure 26: Curves of the stress at the vehicle head over time at different ice thicknesses. Figure 25: Dynamic characteristic curves of the vehicle breaking ice with ice thicknesses of 10 mm and 50 mm. 10 mm or 20 mm thick, the hole made by the vehicle after breaking the ice is approximately rectangular. When the ice is above 30 mm thick, the hole is nearly circular. The above phenomenon can be explained from two aspects: the nonlinear mechanical properties of ice and the types of stress waves. (1) Since ice transforms from a ductile material into a brittle material in the process of being broken, the thicker the ice, the slower the transformation. Therefore, it takes a longer time to reach the critical point of the transformation in the process of breaking the ice. When the vehicle breaks ice, the ice is in two states at the same time, that is, ductility and brittleness. The thicker the ice, the more uneven the distribution of the two states and the more noticeable the nonlinear effect is. In practice, the thinner ice is subject to a lower nonlinear effect, so the hole made on it is more perfectly rectangular. Differently, the thicker ice is under a higher nonlinear effect, which causes the irregular edges of the hole and makes it appear circular. (2) When the ice layer is thin, the impact energy of the vehicle on the ice layer is mainly transmitted through bending stress waves. For thicker ice layers, the impact energy is mainly transmitted through compression waves around the collision point, causing high compressive stress on the lower surface of the ice layer and triggering conical radial cracks. The compression waves are reflected as tensile waves on the upper surface of the ice layer, causing layer cracks. The two types of cracks expand and merge to form an approximately circular hole. Figure 27: _Cont._  
In the process of breaking ice, the vehicle is exposed to a very high impact load, which transfers axially along it. To fully reflect the mechanical state of the vehicle in the process of breaking ice, an axial distance is defined to be from a point on the vehicle to the vertex of the vehicle head. Six points are selected with their axial distance of 0 mm, 20 mm, 40 mm, 60 mm, 80 mm, and 100 mm as shown in Figure 28.  
The vehicle is subject to different stresses at different times, but there is always the maximum stress. The relationship of the maximum stress with axial distance and ice thickness is illustrated in Figure 29. It is noticed that the maximum stress occurs at the vertex of the vehicle head, and then declines axially, but goes up near the middle of the vehicle (with an axial distance of 60 mm). This is attributed to the transfer of impact load and the inertial effect: (1) The vehicle is exposed to a large impact load during its collision with ice, and stress first appears at its head. Subsequently, the stress is transferred axially along the vehicle in the form of wave.