## 5 Conclusions  
Aiming at the problem of the multi-physics field coupling effect in the process of a water-exiting vehicle breaking ice, this paper presented an FEM-SPH-SALE coupling algorithm, which combines the high computational efficiency of the FEM with the applicability of the SPH to resolve the problem of deformation and damage. An experiment of the vehicle breaking ice was carried out with different ejection pressures. The accuracy of the proposed FEM-SPH-SALE coupling algorithm was verified by virtue of the four-point ice bending simulation, wedge-body water-entry simulation, and vehicle breaking ice experiment. In this way, we explored the influence of ice thickness and the vehicle's initial velocity on the motion characteristics, load characteristics, and flow field evolution of the vehicle. Some conclusions are mainly drawn as follows:  
1. When the ice thickness is 200 mm, and the ejection pressure is 3 MPa, 4 MPa, and 5 MPa, after breaking ice, the velocity of the vehicle decreases from 13.08 m/s, 15.44 m/s, and 16.63 m/s to 7.80 m/s, 10.62 m/s, and 11.53 m/s, respectively. The velocity loss rate of the vehicle in the process of breaking ice decreases with the increasing initial velocity of the vehicle. 2. When the ice thickness increases from 10 mm to 50 mm, the residual velocity of the vehicle after breaking ice drops from 35.9 m/s to 21.6 m/s, the velocity loss rate goes up from 10.3% to 46.0%, and the maximum stress at the head rises from 9.48 \(\times\) 10\({}^{7}\) Pa to 1.56 \(\times\) 10\({}^{8}\) Pa. The velocity loss rate of the vehicle and the maximum stress at the head become larger with the increase in ice thickness. The influence of ice thickness on the acceleration of the vehicle is mainly reflected in the duration of acceleration but not the peak of acceleration. 3. When the vehicle passes through ice of 10 mm thickness at an initial velocity of more than 70 m/s, the velocity loss rate reaches convergence. The acceleration of the vehicle and the maximum stress at the head increase with the rise of the initial velocity. When the initial velocity is 80 m/s, the maximum acceleration of the vehicle in the process of breaking ice is 47,320 m/s\({}^{2}\), and the maximum stress at the head is 1.70 \(\times\) 10\({}^{8}\) Pa.
4. At the early stage of ice-breaking, the vehicle head intrudes into the ice and causes a small amount of broken ice in the vicinity of the collision point. With the motion of the vehicle, the central part of the ice is \"pushed upwards\", and a large amount of broken ice moves upwards with the vehicle. The amount of broken ice increases with the thickness of the ice. Figure 37: Sensitivity analysis of the initial velocity and ice thickness. * Due to the transmission of stress wave and inertial effect, the stress on the vehicle in the process of breaking ice tends to \"decrease, increase, and then decrease\" axially from the vertex of the vehicle head. Therefore, when designing a water-exiting vehicle, it is necessary to reinforce the structure of the head and middle sections of the vehicle. * When the vehicle breaks ice, the air cavities at the head collapse under the squeeze of the ice, and those in the cylindrical section of the vehicle repeat the process of \"generation/collapse\", which results in the phenomenon of intensive cavitation. * When ice reaches the critical strain and transforms into SPH particles, the interaction between a large number of high-speed SPH particles and the fluid will cause pressure oscillations, energy dissipation, and tensile instability phenomena, which will become an important issue in future research. Conceptualization, Z.D. and D.F. ; methodology, Z.D. and D.F. ; software, Z.D., D.F. and J.C.; validation, Z.D., D.F. and J.C.; formal analysis, Z.D. and D.F. ; investigation, Z.D. and J.C.; resources, D.F. ; writing--original draft preparation, Z.D. ; writing--review and editing, Z.D. and D.F. ; visualization, D.F. and J.C.; supervision, D.F. ; project administration, D.F.