## 1 Introduction  
The polar region is rich in natural resources and of extremely high strategic value [1, 2, 3]. The use of water-exiting vehicles for underwater resource exploration in polar regions has broad application prospects. However, the presence of ice in the polar region poses a huge challenge to the floating up and recycling of water-exiting vehicles. For this reason, the vehicle must be capable of breaking ice while undertaking such missions as resource detection and terrain exploration. The water-exiting vehicle breaking ice is a forcible nonlinear dynamic response, which involves structural failure of the vehicle and ice crack propagation. For this reason, it is characterized by material nonlinearity, geometrical nonlinearity, and contact nonlinearity. To meet the practical needs of vehicles in the polar region, it is of great significance to explore the coupling effect on the water-exiting vehicle breaking ice. As a typical solid substance, the mechanical properties of ice are affected by multiple factors such as temperature, salinity, and crystal structure [4; 5; 6]. Building an accurate and reliable constitutive model for ice material lays a foundation for delving into the interaction of the vehicle and ice. Hence, scholars have explored extensively in this field. The elastic/plastic constitutive model is a one-dimensional model based on plasticity, which has been widely applied in the simulation of ice. [PERSON] et al. [7] combined peridynamic and adaptive dynamic relaxation to establish a peridynamic elastic/plastic constitutive model for ice material. After comparing the three-point bending experimental results with the numerical simulation results, they proved that the model delivered an accurate simulation of the ice material damage process without adding any extra rules on damage. Based on the principle of empirical failure, [PERSON] et al. [8] put forward an elastic/plastic ice material model and introduced a cutting-plane algorithm to describe the plastic stress/strain relationship. Furthermore, they adopted a user-defined procedure to embed the model into the LS-DYNA software. The elastic/plastic constitutive model provides a satisfying simulation of ice plasticity damage, but it ignores such characteristics of ice material as strain rate effect, tension, and compression. For this reason, [PERSON] et al. [9] presented a new sea ice model that takes into account strain sensitivity to flow stress, independent failure stress in compression, and ice's capability of bearing hydrostatic pressure after failure. [PERSON] et al. [10] proposed a phenomenological model based on strain rate correlation to capture the ductile/brittle transition behavior of ice under loading, which was verified by a rigid indentation test. In order to better describe the crack expansion of ice when it is damaged, some scholars have developed a variety of constitutive models based on the theories related to fracture mechanics. [PERSON] et al. [11] adopted a Johnson-Holmquist-2 constitutive model to illustrate the characteristics of ice material. While taking into account the damage mode of ice material, they determined the relevant parameters of the model through theoretical analysis and experiment and performed the uniaxial compression numerical simulation to prove that the Johnson-Holmquist-2 constitutive model could accurately simulate the damage to sea ice. [PERSON] et al. [12] proposed an ice model based on the Lemaitre damage pattern, which could reflect the microstructure of ice and physical effects under load. [PERSON] et al. [13] employed the explicit finite element method and introduced the Crushable Foam and Drucker-Prager yield criteria to develop a model for ice material with yield strength, damage mode, and dynamic strain rate. This model could accurately predict the contact force. [PERSON] et al.