## 1 Introduction
[14] obtained the variation curve of ice load through a separated Hopkinson pressure bar (SHPB) experiment and established an ice constitutive model containing fracture strength and damage evolution parameters using ABAQUS 2022 software. Presently, the studies on structures breaking ice could be categorized into three focuses: structures breaking ice in a waterless environment, structures breaking ice and entering water, and structures breaking ice and exiting water. Without the effect of fluid, the first focus can be easily addressed in experiments and simulations. [PERSON] et al. [15] built a numerical computation model for a rigid sphere bounding the ice and obtained ice damage results with different sphere speeds, ice thicknesses, and boundary conditions. As revealed in the results, when the speed of the sphere increases, the damage to the ice changes from several non-penetrating radial cracks to a mesh of radial and circumferential cracks. [PERSON] et al. [16] studied the interaction between a six-degree-of-freedom ship and ice ridges using bending and crushing failure modes to simulate ice loads. [PERSON] et al. [17] carried out an experiment to study the crack pattern and damage mechanism of an ice sample subject to vertical impact and found that when the damage caused by the impact head to the ice sample is more severe, the impact load applied to the ice sample is lower if the size of the ice sample and the kinetic energy of the impact are identical. As for the problem of structures breaking ice and entering water, [PERSON] et al. [18] constructed a numerical computation model for a rigid sphere breaking ice and entering water based on the Boundary Data Immersion Method (BDIM) and Volume of Fluid (VOF). The results show that the motion characteristics of the sphere is affected by the impact speed, the density of the rigid sphere, and the elastic modulus of ice. [PERSON] et al. [19] delved into the influence of head shape and length-to-diameter ratio on ice damage when a vehicle breaks ice and enters water. They noticed that the water environment has little effect on the pattern of ice damage but greater effect on the velocity and acceleration of the vehicle in motion. [PERSON] et al. [20] established a numerical model for the high-speed water entry projectiles based on the coupled Euler-Lagrange (CEL) method. They compared and analyzed the evolution of cavitation in the presence and absence of ice and obtained the effect of ice sheet on the load characteristics of structures. At present, the main focus of scholars is the structures breaking ice and exiting water by virtue of test and simulation. [PERSON] et al. [21] explored the influence of broken ice on the hydrodynamic properties of a water-exiting vehicle. As shown in the results, the deflection angle of the vehicle at the time of exiting water with ice floating around is greater than that without ice around, and the pressure around the vehicle fluctuates more violently when the vehicle approaches the ice/water interface. [PERSON] et al. [22] put forward a new algorithm combining the BDIM and VOF and used it in the numerical calculation of a semispherical vehicle breaking ice and exiting water. They pointed out that the shear effect of fluid must be the main cause for the cavitation of a vehicle. [PERSON] et al. [23] carried out a numerical simulation for a vehicle breaking ice at different initial velocities and concluded that the load characteristics of the vehicle relate to its velocity and the mechanical properties of ice. Some mesh-based numerical simulation methods have been widely applied in various fields such as the Finite Element Method (FEM) and Finite Volume Method (FVM), but they have certain limitations in simulating the interaction between structures and ice. These limitations are mainly reflected in two aspects: (1) Ice has a large deformation structurally under the impact of a high-speed vehicle, which leads to mesh distortion and undermines the accuracy of solution.