## 1 Introduction
(2) Ice cracks extensively under impact, but cracks exist only along the mesh border in the mesh-based methods, which does not match with the practical conditions. Mesh-free methods have become popular in recent years. At the time of computation, these methods need only nodes but do not rely on the link between nodes, so they are greatly adaptive and applicable to addressing the mutual effect of structures and ice [24; 25; 26]. Smoothed particle hydrodynamics (SPH) is currently the fastest spreading mesh-free method. After being first put forth by [PERSON] et al. [27], the SPH method has been widely applied in such domains as hydrodynamics and impact dynamics. In the method, particles carry the properties of material, including energy and density, so that it is differentiated from other mesh-free methods that take nodes only for interpolation in computation. For this reason, the SPH method can deliver more accurate tracking of material interface and deformation boundary and has been applied to a certain extent in the field of structural-ice interaction. [PERSON] et al. [28] introduced fracture criteria into the SPH method and performed numerical simulations of three-point bending tests on ice, proving the feasibility of the SPH method in solving fracture problems. [PERSON] et al. [29] built a vehicle/water/ice numerical model based on the SPH method to explore the ice resistance to an icebreaker in various circumstances. [PERSON] et al. [30] adopted the SPH method to simulate the collision of a vertical cylindrical structure with broken ice and studied the effect of such parameters as ice thickness and density on ice resistance. The SPH method may better simulate the crack spread of sea ice under impact and ensure higher accuracy of computation, but it is less efficient in computation and occupies more computing resources than the mesh-based methods. Therefore, the SPH and FEMcoupling algorithm will be practically more effective since it takes into account both accuracy and efficiency of computation. [PERSON] et al. [31] utilized the SPH-FEM adaptive coupling algorithm to simulate the mutual effect of horizontal ice and inclined structure. As revealed in the results, the algorithm, which keeps the strengths of both SPH and FEM methods, can greatly simulate the large deformation of ice and guarantee the accuracy of computation. [PERSON] et al. [32] proposed an SPH-FEM coupling algorithm to simulate the collision of structure and floating ice at sea, and adopted the [PERSON] failure criterion to reflect the damage to sea ice with the SPH method for the outer layer and the FEM method for the inner layer of floating ice. To sum up, scholars have currently conducted extensive research on the lateral ice breaking of structures along the sea level (e.g., ships and vertical structures breaking ice) [33] and the hydrodynamics of structures passing through the mixture of ice and water. However, they have rarely studied the mechanical response and motion characteristics of structures surfacing and breaking ice. In the meantime, most of their studies adopt the mesh-based methods, leading to poor computational accuracy. The experiment provides the significant basis for verifying the accuracy of the simulation model, but there is not much experimental data available for the vehicles breaking ice at high velocity. In response to the shortcomings of current research, the main contributions of this paper are as follows: (1) In response to the low accuracy of traditional grid methods, this paper combined the FEM-SPH adaptive algorithm with the S-ALE algorithm to propose an FEM-SPH-SALE coupling algorithm suitable for multi-physics field calculations; based on the algorithm, a numerical computation model was constructed for a water-exiting vehicle breaking ice, and the Johnson-Holmquist-2 constitutive model was used to simulate the mechanical properties of ice.